, Sums of products of generalized Fibonacci and Lucas numbers, 2007.
, Fibonacci and Lucas Identities from Toeplitz-Hessenberg Matrices, Applications and Applied Mathematics, vol.14, issue.2, p.2019
, , vol.6, 1984.
, The Theory of Determinants in the Historical Order of Development: Volume One: General and Special Determinants Up to 1841. Volume Two: The Period 1841 to 1860, 1960.
, Integer sequences and circle chains inside a hyperbola, Forum Geometricorum, vol.19, pp.11-16, 2019.
, Integer sequences and ellipse chains inside a hyperbola, Annales Mathematicae et Informaticae
, Ellipse chains and the associated integer sequences
, Balancing diophantine triples with distance 1. In Period, Math. Hung, vol.71, issue.1, pp.1-10, 2015.
, (editor). The On-Line Encyclopedia of Integer Sequences
, A q-analogue for bisnomial coefficients and generalized Fibonacci sequences, Comptes Rendus Mathematique, vol.352, issue.3, pp.167-171, 2014.
, Connection between bisnomial coefficients and their analogs and symmetric functions, Turkish Journal of Mathematics, vol.42, issue.3, pp.807-818, 2018.
, Connection between ordinary multinomials, Fibonacci numbers, Bell polynomials and discrete uniform distribution, Annales Math. et Informaticae, vol.35, pp.21-30, 2008.
, Combinatorial identities for the r-Lah numbers, Ars Comb, vol.115, pp.453-458, 2014.
, Cross recurrence relations for r-Lah numbers, Ars Comb, vol.110, pp.199-203, 2013.
, Companion sequences associated to the r-Fibonacci sequence: algebraic and combinatorial properties, Turkish Journal of Mathematics, vol.28, issue.7-8, pp.1095-1114, 2017.
, Linear recurrent sequences and powers of a square matrix, p.17, 2006.
, A new generalization of Fibonacci and Lucas p-numbers, Journal of computational analysis and applications, vol.25, issue.4, pp.657-669, 2018.
, Some applications of universal algebra, In Colloq. Math. Soc. Janos Bolyai, vol.29, pp.107-128, 1977.
, Median algebras acting on sets, Algebra Universalis 29, pp.477-484, 1992.
, Median algebras. Discrete mathematics, vol.45, pp.1-30, 1983.
, Ternary boolean algebra, Bull. Amer. Math. Soc, vol.53, pp.567-572, 1947.
, A ternary operation in distributive lattices, Bull. Amer. Math. Soc, vol.53, pp.749-752, 1947.
, Medians, lattices, and trees, Proc, vol.5, pp.808-812, 1954.
, Trees, lattices, order, and betweenness, Proc. Am. Math. Soc, vol.3, issue.3, pp.369-381, 1952.
, The ternary operation (abc) = ab ?1 c of a group, Bull. Amer. Math. Soc, vol.49, pp.869-877, 1943.
, Flocks, groups and heaps, joined with semilattices. Quasigroups and Related Systems 24, pp.43-66, 2016.
, Wagner's Theory of Generalised Heaps, 2017.
, Classification of P-oligomorphic groups, conjectures of Cameron and Macpherson, 2020.
URL : https://hal.archives-ouvertes.fr/tel-02420262
, Oligomorphic permutation groups, London Mathematical Society Lecture Note Series, vol.152, 1990.
, The orbit algebra of a permutation group with polynomial profile is Cohen-Macaulay, 30th International Conference on Formal Power Series and Algebraic Combinatorics, vol.2018, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01763795
, The Sage Developers. SageMath, the Sage Mathematics Software System, vol.9, p.2020
, GAP -Groups, Algorithms, and Programming, 1999.
, Enumerating subgroups of the symmetric group, 2010.
, Quelques exemples de suites unimodales en théorie des nombres, Journal de théorie des nombres de Bordeaux, pp.13-30, 1990.
, Unimodal rays in the regular and generalized Pascal triangles, J. of Integer Seq, vol.11, 2008.
, Les nombres de Stirling associés avec succession d'ordre 2, nombres de Fibonacci-Stirling et unimodalité, C. R. Acad. Sci. Paris, Ser. I, 2015.
, The t-successive associated Stirling numbers, t-Fibonacci Stirling numbers and Unimodality, Turkish Journal of Mathematics, pp.1279-1291, 2017.
, Sur une propriétés des polynômes à racines négatives, Journal de mathématiques pures et appliqués, vol.75, issue.2, pp.85-105, 1996.
, Unimodal, log-convave and Polyà frequency sequences in combinatorics, vol.413, 1989.
, Location of the maximum Stirling number(s) of second kind, Studies in App Math, vol.59, pp.83-93, 1978.
, Stirling behaviour is asymptotically normal, Ann. Math. Stat, vol.38, pp.410-414, 1967.
, Log-concave and unimodal sequences in Algebra, Combinatorics and Geometry, Annals of the New York academy of sciences, vol.576, issue.1, pp.500-535, 1989.
, On unimodality sequence of binomial coefficients, Discrete Math, vol.9, pp.79-89, 1974.
, Log-concavity of principal diagonal rays in the regular Lah triangles, Ars Combinatorias, vol.114, pp.75-83, 2018.
, A characterization of quasitrivial n-semigroups
, Bands of semigroups, Proc. Amer. Math. Soc, vol.5, pp.499-504, 1954.
, The algebraic theory of semigroups, vol.1, 1961.
, Every quasitrivial n-ary semigroup is reducible to a semigroup, Algebra Universalis, vol.80, issue.4, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02099236
, Reducibility of n-ary semigroups: from quasitriviality towards idempotency, 2019.
, Characterizations of quasitrivial symmetric nondecreasing associative operations, Semigroup Forum, vol.98, pp.154-171, 2019.
, On the structure of symmetric n-ary bands
, On n-ary semigroups with adjoint neutral element, Quasigroups and Related Systems, vol.14, pp.163-168, 2006.
, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z, vol.29, pp.1-19, 1928.
, Commutative semigroups, 2001.
, Automorphisms of polyadic automata, J. Assoc. Comput. Mach, vol.16, pp.208-219, 1969.
, Fundamentals of semigroup theory, 1995.
, Associative idempotent nondecreasing functions are reducible, Semigroup Forum, vol.98, pp.140-153, 2019.
, Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines, Trans. Amer. Math. Soc, vol.116, pp.450-464, 1965.
, The free algebra in the variety generated by quasi-trivial semigroups, Semigroup Forum, vol.20, pp.151-156, 1980.
, Discrete mathematics using latin squares, 1998.
, D-dimensional hypercubes and the Euler and MacNeish conjectures, Montsh. Math, vol.111, pp.223-238, 1995.
, On associative operations on commutative integral domains, Semigroup Forum, vol.100, issue.3, pp.910-915, 2020.
, Idempotent semigroups, Amer. Math. Monthly, vol.61, pp.110-113, 1954.
, Introduction to semigroups, 1973.
, Lectures in semigroups, 1977.
, Polyadic groups, Trans. Amer. Math. Soc, vol.48, pp.208-350, 1940.
, An Introduction to the Theory of Groups, 1995.
, The submaximal clones on the three-element set with finitely many relative R-classes, Discuss. Math. Gen. Algebra Appl, vol.30, pp.7-33, 2010.
, Clones with finitely many relative R-classes, Algebra Universalis, vol.65, pp.109-159, 2011.
, Partial orders induced by quasilinear clones, Contributions to General Algebra 20, Proceedings of the Salzburg Conference 2011 (AAA81), pp.51-84, 2012.
, Galois theory for minors of finite functions, Discrete Math, vol.254, pp.405-419, 2002.
, The Two-Valued Iterative Systems of Mathematical Logic, Annals of Mathematics Studies, issue.5, 1941.
, Polynomial-time algorithms for checking some properties of Boolean functions given by polynomials, Theory Comput. Syst, vol.58, pp.383-391, 2016.
, On the number of clonoids, Algebra Universalis, vol.80, issue.4, p.pp, 2019.
, Mémoire sur les combinaisons régulière et leurs applications, Annales scientifique de l'ENS. 2 eme série, pp.155-198, 1876.
, Connection between bi s nomial coefficients and their analogs and symmetric functions, Turkish Journal of Mathematics, vol.42, pp.807-818, 2018.
, Congruence properties for bi s nomial coefficients and like extended Ram and Kummer theorems under suitable hypothesis, Mediterranean Journal of Mathematics, vol.17, p.36, 2020.
, Generalized Pascal triangle and Pyramids, their fractals graphs and applications. The Fibonacci Association, 1993.
, From entanglement witness to generalized Catalan numbers, Scientific Reports, vol.6, p.30232, 2016.
, Spin Multiplicities, Physics letter A, vol.381, pp.422-427, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01345527
, The Doctrine of Chances, 1967.
, De evolutione potestatis polynomialis cuiuscunque (1+x+x 2 +· · · ) n, Nova Acta Academiae Scientarum Imperialis Petropolitinae, vol.12, pp.28-40
, Observationes analyticae, Novi Commentarii Academiae Scientarum Petropolitanae, Opera Omnia, Series, vol.11, pp.50-69
, Restricted Occupancy Theory A Generalization of Pascal's Triangle, The American Mathematical Monthly, vol.63, issue.1, pp.20-27, 1956.
, Solutio quaestionis, quot modis polygonum n laterum in polygona m laterum, per diagonales resolvi quaeat. Nova acta academiae scientiarum imperialis Petropolitanae, vol.9, pp.243-251, 1791.
, Super ballot numbers, Journal of Symbolic Computation, vol.14, pp.179-194, 1992.
, A combinatorial interpretation of the numbers 6(2n)!n!(n + 2)!, Journal of Integer Sequences, vol.8, 2005.
, Concrete Mathematics, 1994.
, Fibonacci and Catalan numbers An introduction, 2012.
, Higher Algebra: a Sequel to Elementary Algebra for Schools, p.1894
, Catalan numbers, their generalization, and their uses, The Mathematical Intelligencer, vol.13, pp.64-75, 1991.
, Generalized Catalan number, sequences and polynomials, Turkish Journal of Mathematics, vol.34, pp.441-449, 2010.
, Catalan Numbers with Applications, 2009.
, Some Combinatorial Interpretations and Applications of Fuss-Catalan Numbers, International Scholarly Research Network ISRN Discrete Mathematics, article ID 534628, 2011.
, Functional composition patterns and power series reversion, vol.94, pp.441-451, 1960.
, The On-Line Encyclopedia of Integer Sequences
, Catalan numbers, 2015.
, Automatic Sequences: Theory, Applications, Generalizations, vol.ISBN, pp.0-521, 2003.
, , vol.79, p.pp, 2018.
, Combinatorics, automata, and number theory. Encyclopedia of Mathematics and its Applications. 135. 2010
, On longest induced paths in graphs. Chinese Quart, J. Math, vol.3, issue.3, pp.61-65, 1968.
, The theory of 2-structures. A framework for decomposition and transformation of graphs, 1999.
, Substitutions in dynamics, arithmetics and combinatorics, 2002.
, With an appendix by Norbert Sauer, Studies in Logic and the Foundations of Mathematics, vol.145, 2000.
, intervalle en théorie des relations, ses généralisations, filtre intervallaires et clôture d'une relation, Orders, description and roles, vol.23, pp.343-358, 1984.
, Perfect graphs, vol.18, pp.25-66, 1967.
, Ordering by divisibility in abstract algebras, Proc. London Math. Soc, vol.3, pp.326-336, 1952.
, A characterization of the indecomposable and infinite graphs, Glob. J. Pure Appl. Math, vol.3, pp.272-285, 2005.
, Comparability graphs, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci, vol.147, pp.3-40, 1985.
, Jónsson posets and unary Jónsson algebras, Algebra Universalis, vol.69, issue.2, pp.101-112, 2013.
, Über eine Schlussweise aus dem Endlichen ins Unendliche, Acta Sci. Math. (Szeged), issue.3, pp.121-130, 1927.
, Orthogonal countable ordinals, vol.335, pp.35-44, 2014.
, Finite and Infinite Words, Algebraic Combinatorics on Words (Encyclopedia of Mathematics and its Applications, pp.1-44, 2002.
, Symbolic Dynamics II. Sturmian Trajectories. American Journal of Mathematics, vol.62, pp.1-42, 1940.
, Sur l'énumération de structures discrètes: une approche par la théorie des relations, 2015.
, Graphs Without Isometric Rays and Invariant Subgraph Properties, I, Journal of Graph Theory, vol.27, issue.2, pp.99-109, 1998.
, Un belordre d'abritement et ses rapports avec les bornes d'une multirelation, Comptes rendus Acad. Sci. Paris, vol.274, pp.1677-1680, 1972.
, Sur la théorie des relations, 1978.
, Relation minimale pour son âge, Zeitsch. f. math. Logik und Grundlag d, Math. Bd, vol.25, pp.315-344, 1979.
, On Minimal Prime Graphs and Posets, Order, vol.16, pp.357-375, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00863170
, Structure d'ordre de la collection des âges de relations, 1992.
, Sur les âges de relations et quelques aspects homologiques des constructions D+M, 2002.
, Graphs indecomposable with respect to the X-join, Discrete Math, vol.6, pp.281-298, 1973.
, Infinite paths that contain only shortest paths, Journal of Combinatorial Theory, Series B, vol.41, issue.3, pp.341-355, 1986.
, On the poset of computation rules for nonassociative calculus, Order, vol.30, issue.1, pp.269-288, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00787750
, On integer-valued means and the symmetric maximum, Aequationes Mathematicae, vol.91, issue.2, pp.353-371, 2017.
URL : https://hal.archives-ouvertes.fr/halshs-01412025
, The Möbius transform on symmetric ordered structures and its application to capacities on finite sets, Discrete Mathematics, vol.287, issue.1-3, pp.17-34, 2004.
, Integer valued means, Aequationes Mathematicae, vol.88, pp.137-149, 2014.
, Atti delle Reale Accademia Nazionale dei Lincei Mem, Cl. Sci. Fis. Mat. Natur. Sez, vol.12, pp.323-343, 1930.
, Simple permutations and pattern restricted permutations, Discrete Mathematics, vol.300, pp.1-15, 2005.
, Hereditary properties of partitions, ordered graphs and ordered hypergraphs, European Journal of Combinatorics, vol.8, pp.1263-1281, 2006.
, Hereditary properties of ordered graphs, Topics in discrete mathematics, vol.26, pp.179-213, 2006.
, Hereditary properties of tournaments, Electron. J. Combin, vol.14, issue.1, p.25, 2007.
, The unlabelled speed of a hereditary graph property, J. Combinatorial Theory, series B, vol.99, pp.9-19, 2009.
, The morphology of infinite tournaments; application to the growth of their profile, European Journal of Combinatorics, vol.31, pp.461-481, 2010.
, Homogeneous permutations. Permutation patterns (Otago, 2003), Electron. J. Combin, vol.9, issue.2, 2002.
, Theory of relations, 2000.
, Quelques problèmes combinatoires concernant les ordres totaux et les relations monomorphes, Annales Institut Fourier Grenoble, vol.15, pp.415-524, 1965.
, Détermination du degré optimal d m de monomorphie pour les structures relationnelles au plus m-aires, vol.12, pp.141-146
, A class of incidence matrices, Proc. Amer. Math. Soc, vol.17, pp.1233-1237, 1966.
, The uncountable spectra of countable theories, Ann. of Math, issue.2, pp.207-257, 2000.
, Ordering by divisibility in abstract algebras, Proc. London Math. Soc, vol.2, issue.3, pp.326-336, 1952.
, On growth rates of closed permutation classes, Electron. J. Combin, vol.9, issue.2, p.pp, 2002.
, On incidence matrices of finite projection and affine spaces, Math.Zeitschrift, vol.124, pp.315-318, 1972.
, On growth rates of permutations, set partitions, ordered graphs and other objects, Electron. J. Combin, vol.15, issue.1, p.pp, 2008.
, Overview of general results in combinatorial enumeration, in Permutation patterns, London Math. Soc. Lecture Note Ser, vol.376, pp.3-40, 2010.
, Sur la détermination d'une relation par les types d'isomorphie de ses restrictions, C. R. Acad. Sci. Paris Sér. A-B, vol.275, pp.951-953, 1972.
, L'indéformabilité des relations et multirelations binaires, Z. Math. Logik Grundlag. Math, vol.24, issue.4, pp.303-317, 1978.
, Excluded permutation matrices and the Stanley-Wilf conjecture, J. Combin. Theory, Ser. A, vol.107, pp.153-160, 2004.
, From the complexity of infinite permutations to the profile of bichains, ROGICS'08: International Conference on Relations, Orders and Graphs: Interaction with Computer Science, pp.1-6, 2008.
URL : https://hal.archives-ouvertes.fr/lirmm-00434328
, Université des sciences et de la technologie Houari Boumediene
, Profile and hereditary classes of relational structures, Proceedings ISOR'11, International Symposium on Operational Research, p.3, 2011.
, Décomposition monomorphe des structures relationelles et profil de classes héréditaires, vol.7, p.2014
, Profile and hereditary classes of relational structures, J. of MVLSC, vol.27, issue.5-6, pp.475-500, 2016.
, Hereditary classes of ordered binary structures, preprint, 28pp. dec, 2018.
, Un belordre d'abritement et ses rapports avec les bornes d'une multirelation, Comptes rendus Acad. Sci. Paris, Sér A, vol.274, pp.1677-1680, 1972.
, Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux relations, Math. Zeitschr, vol.150, issue.2, pp.117-134, 1976.
, Sur la théorie des relations, 1978.
, Relation minimale pour son âge, Z. Math. Logik Grundlag. Math, vol.25, pp.315-344, 1979.
, The asymptotic behavior of a class of counting functions, Annals of Discrete Math, vol.79, pp.223-224, 1980.
, Relation impartible, Dissertationnes, vol.103, pp.1-48, 1981.
, Application de la notion de relation presque-enchaînable au dénombrement des restrictions finies d'une relation, Z. Math. Logik Grundlag. Math, vol.27, pp.289-332, 1981.
, The profile of relations, Proceedings of the 14 th symposium of the Tunisian Mathematical Society, vol.2, pp.237-272, 2006.
, Some relational structures with polynomial growth and their associated algebras I: Quasi-polynomiality of the profile, Electron. J. Combin, vol.20, issue.2, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01121195
, Classification theory and the number of nonisomorphic models, vol.92, 1990.
, Indécomposabilité des graphes et des tournois, 2009.
, Imed Boudabbous and Maurice Pouzet. Inversion dans les tournois, C.R. Acad. Sci. Paris, Ser. I, vol.348, pp.703-707, 2010.
, Imed Boudabbous and Maurice Pouzet. Inversions in tournaments. Unpublished manuscript, 2012.
, The minimum rank of symmetric matrices described by a graph: a survey, Linear Algebra and its Applications, vol.426, issue.2-3, pp.558-582, 2007.
, Symplectic embeddings of graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, vol.2, pp.193-207, 1987.
, Chromatic number and the 2-rank of a graph, Journal of Combinatorial Theory, Series B, vol.81, issue.1, pp.142-149, 2001.
, Boolean dimension of a graph and inversions in tournaments, Workshop in honor of Michel Habib, 2017.
, Stirling and eulerian numbers of types B and D, Proceedings of the 11th International Conference on Random and Exhaustive Generation of Combinatorial Structures, vol.2113, pp.53-59, 2018.
, The canonical join complex, 2016.
, Orderings of Coxeter groups, Combinatorics and Algebra, vol.34, pp.175-195, 1983.
, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol.231, 2005.
, Combinatorics of permutations. Discrete Mathematics and its Applications, 2012.
, Permutohedra and associahedra, Lattice theory: special topics and applications, vol.2, pp.215-286, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01700866
, Aggregation of inequalities in integer programming, Studies in integer programming (Proc. Workshop, vol.1, pp.145-162, 1975.
, Free hyperplane arrangements between A n?1 and B n, Math. Z, vol.215, issue.3, pp.347-365, 1994.
, Free Lattices, Mathematical Surveys and Monographs, vol.42, 1995.
, Stirling polynomials, J. Combinatorial Theory Ser. A, vol.24, issue.1, pp.24-33, 1978.
URL : https://hal.archives-ouvertes.fr/hal-00843320
, Analyse algébrique d'un scrutin, Math. Sci. Hum, vol.4, pp.9-33, 1963.
, Threshold graphs and related topics, Annals of Discrete Mathematics, vol.56, 1995.
, The lattice of threshold graphs, JIPAM. J. Inequal. Pure Appl. Math, vol.6, issue.1, 2005.
, Birkhäuser Advanced Texts: Basler Lehrbücher
, , 2015.
, A generalized permutahedron, Algebra Universalis, vol.34, issue.4, pp.496-509, 1995.
, On discrete idempotent paths, Lecture Notes in Comput. Sci, vol.11682, pp.312-325, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02153821
, The continuous weak order, Journal of Pure and Applied Algebra, 2020.
URL : https://hal.archives-ouvertes.fr/hal-01944759
, Generalizations of the permutohedron, Lattice Theory: Special Topics and Applications, vol.2, pp.287-397, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01774635
, The equational theory of the weak Bruhat order on finite symmetric groups, Journal of the European Mathematical Society, vol.20, issue.8, pp.1959-2003, 2018.
, An introduction to hyperplane arrangements, Geometric combinatorics, vol.13, pp.389-496, 2007.
, Cambridge Studies in Advanced Mathematics, vol.1, 2012.
, Some permutation representations of Weyl groups associated with the cohomology of toric varieties, Adv. Math, vol.106, issue.2, pp.244-301, 1994.
, On polymorphism-homogeneous relational structures and their clones, Algebra Universalis, vol.73, issue.1, pp.53-85, 2015.
, Some results and problems related to universal algebraic geometry, Internat. J. Algebra Comput, vol.17, issue.5-6, pp.1133-1164, 2007.
, Solution sets of systems of equations over finite lattices and semilattices. Algebra Universalis, vol.81, p.13, 2020.
, On the shape of solution sets of systems of (functional) equations, Aequationes Math, vol.91, issue.5, pp.837-857, 2017.
, Galois theory for Post algebras. I, II. Kibernetika (Kiev), pp.1-9, 1969.
, Closed systems of functions and predicates, Pacific J. Math, vol.27, pp.95-100, 1968.
, The algebras of partial functions and their invariants, Kibernetika (Kiev), vol.149, issue.2, pp.1-11, 1981.
, Homomorphism-homogeneous relational structures, Combin. Probab. Comput, vol.15, issue.1-2, pp.91-103, 2006.
, Polymorphism-homogeneous monounary algebras, Math. Slovaca, vol.65, issue.2, pp.359-370, 2015.
, Injectives in varieties of groups, Algebra Universalis, vol.14, issue.3, pp.398-400, 1982.
, Injective hulls of semilattices, Canad. Math. Bull, vol.13, pp.115-118, 1970.
, The category of semilattices, Algebra Universalis, vol.1, issue.1, pp.26-38, 1971.
, Remarks on homomorphism-homogeneous lattices and semilattices, Monatsh. Math, vol.164, issue.1, pp.23-37, 2011.
, Projective and injective distributive lattices, Pacific J. Math, vol.21, pp.405-420, 1967.
, Infinite abelian groups, I. Pure and Applied Mathematics, vol.36, 1970.
, Injectivity in varieties of groups, Algebra Universalis, vol.14, issue.3, pp.280-286, 1982.
, Homomorphism-homogeneous monounary algebras, Math. Slovaca, vol.63, issue.5, pp.993-1000, 2013.
, Retract injective and retract projective monounary algebras, Contributions to general algebra, 10 (Klagenfurt, 1997), pp.207-214, 1998.
, Syntactic Structures. The Hague: Mouton, 1957.
, Dependency parsing with graph rewriting, Proceedings of the 14th International Conference on Parsing Technologies, IWPT 2015, pp.30-39, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01188694
, Word ordering as a graph rewriting process, Formal Grammar -20th and 21st International Conferences, vol.9804, pp.216-239, 2015.
URL : https://hal.archives-ouvertes.fr/halshs-01740481
, Application of Graph Rewriting to Natural Language Processing. Logic, Linguistic and Computer Science, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01814386
, Handbook of Graph Grammars and Computing by Graph Transformation: Volume I. Foundations, 1997.
, Graph Structure and Monadic Second-Order Logic, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00646514
, A note on algebraic structure of tree decomposition of graphs, The First Asian Workshop on Programming Languages and Systems, pp.223-229, 2000.
, Interaction nets, Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages, pp.95-108, 1990.
, Strategic port graph rewriting: an interactive modelling framework, Mathematical Structures in Computer Science, vol.29, issue.5, pp.615-662, 2019.
, Drags: A compositional algebraic framework for graph rewriting, Theor. Comput. Sci, vol.777, pp.204-231, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01853138
, Some undecidable termination problems for semi-Thue systems, Theoretical Computer Science, vol.142, pp.257-276, 1995.
, Non-simplifying graph rewriting termination, Proceedings 7th International Workshop on Computing with Terms and Graphs, TERMGRAPH 2013, pp.4-16, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00921053
, Rewrite systems, Formal Models and Semantics, vol.B, pp.243-320, 1990.
, Graph path orderings, LPAR-22. 22nd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, pp.307-325, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01903086
, Simplification orders for term graph rewriting, Mathematical Foundations of Computer Science, pp.458-467, 1997.
, Matrix interpretations for proving termination of term rewriting, Journal of Automated Reasoning, vol.40, issue.2, pp.195-220, 2008.
, A note on simplification orderings, Information Processing Letters, pp.212-215, 1979.
, Elements of Automata Theory, 2009.
, Behavioural differential equations: a coinductive calculus of streams, automata, and power series, Theoretical Computer Science, vol.308, issue.1, pp.1-53, 2003.
, Proving termination with multiset orderings, Commun. ACM, vol.22, issue.8, 1979.
, Equations and rewrite rules: a survey, formal language Theory: perspective and open problems, 1980.
, Transductions rationnelles décroissantes. RAIRO. Informatique théorique, vol.15, pp.141-148, 1981.
, Transducteurs des langages de Chomsky, Ann. Inst. Fourier, Grenoble, vol.18, pp.339-455, 1968.
, Graph minors. XX. Wagner's conjecture, J. Comb. Theory, Ser. B, vol.92, issue.2, pp.325-357, 2004.
, Forbidden directed minors and Kelly-width, Theoretical Computer Science, vol.662, pp.40-47, 2017.
, Profinite methods in automata theory, 26th International Symposium on Theoretical Aspects of Computer Science, vol.3, pp.31-50, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00359677
, Ranking tournaments, SIAM J. Discrete Math, vol.20, pp.137-142, 2006.
, Digraphs: Theory, Algorithms and Applications, 2009.
, On the problem of finding disjoint cycles and dicycles in a digraph, Combinatorica, vol.31, pp.639-668, 2011.
, A polynomial algorithm for the 2-path problem for semicomplete digraphs, SIAM J. Discrete Math, vol.5, pp.366-376, 1992.
,
, Inversion dans les tournois, Comptes Rendus Mathematique, vol.348, issue.13, pp.703-707, 2010.
, The minimum feedback arc set problem is NP-hard for tournaments, Combin. Probab. Comput, vol.16, pp.1-4, 2007.
URL : https://hal.archives-ouvertes.fr/lirmm-00140321
, Primal-dual approximation algorithms for feedback problems in planar graphs, Integer Programming and Combinatorial Optimization, pp.147-161, 1996.
, Reducibility among combinatorial problems, Complexity of computer computations (Proc. Symp, pp.85-103, 1972.
, Intercyclic digraphs, Proceedings of a AMS-IMS-SIAM Joint Summer Research Conference on Graph Minors, vol.147, pp.203-245, 1991.
, Minimum transversal of cycles in intercyclic digraphs, 1989.
, Combinatorica, vol.16, issue.4, pp.535-554, 1996.
, The gallai-younger conjecture for planar graphs, Combinatorica, vol.16, issue.4, pp.555-566, 1996.
, On feedback problems in digraphs, WG 1989, vol.411, pp.218-231, 1989.
,
, Linked data -the story so far, Int. J. Semantic Web Inf. Syst, vol.5, issue.3, pp.1-22, 2009.
, Semantic web in data mining and knowledge discovery: A comprehensive survey, J. Web Semant, vol.36, pp.1-22, 2016.
, Canonicalizing open knowledge bases, Proceedings of the 23rd ACM International Conference on Conference on Information and Knowledge Management, CIKM, pp.1679-1688, 2014.
, Generating possible interpretations for statistics from linked open data, The Semantic Web: Research and Applications -9th Extended Semantic Web Conference, ESWC 2012, vol.7295, pp.560-574, 2012.
, Discriminative predicate path mining for fact checking in knowledge graphs, Knowl.-Based Syst, vol.104, pp.123-133, 2016.
, The Semantic Web, Scientific American, vol.284, issue.5, pp.28-37, 2001.
, A translation approach to portable ontology specifications, Knowledge Acquisition, vol.5, issue.2, pp.199-220, 1993.
, Managing and Mining Graph Data, volume 40 of Advances in Database Systems, 2010.
, PGxO and PGxLOD: a reconciliation of pharmacogenomic knowledge of various provenances, enabling further comparison, BMC Bioinformatics, issue.4, p.20, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02103899
, Application of Graph Rewriting to Natural Language Processing, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01814386
, Querying graph patterns, Proceedings of the 30th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, PODS 2011, pp.199-210, 2011.
, A fast and simple graph kernel for RDF, Proceedings of the International Workshop on Data Mining on Linked Data, with Linked Data Mining Challenge collocated with the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECMLPKDD 2013), vol.1082, 2013.
, Substructure counting graph kernels for machine learning from RDF data, J. Web Semant, vol.35, pp.71-84, 2015.
, AMIE: association rule mining under incomplete evidence in ontological knowledge bases, International World Wide Web Conferences Steering Committee / ACM, pp.413-422, 2013.
, Modeling paths for explainable knowledge base completion, Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP, pp.147-157, 2019.
, Unsupervised generation of data mining features from linked open data, 2nd International Conference on Web Intelligence, Mining and Semantics, WIMS '12, vol.31, 2012.
, Inducing a decision tree with discriminative paths to classify entities in a knowledge graph, Proceedings of the 4th International Workshop on Semantics-Powered Data Mining and Analytics colocated with the 18th International Semantic Web Conference (ISWC 2019), vol.2427, 2019.
, Mining generalized association rules, Proceedings of 21th International Conference on Very Large Data Bases, vol.95, pp.407-419, 1995.
, Raising, to enhance rule mining in web marketing with the use of an ontology, Data Mining with Ontologies: Implementations, Findings, and Frameworks, pp.18-36, 2008.
, Using taxonomies to facilitate the analysis of the association rules, 2011.
, Knowledge-based interactive postmining of association rules using ontologies, IEEE Trans. Knowl. Data Eng, vol.22, issue.6, pp.784-797, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00459393
, Rdf2vec: RDF graph embeddings for data mining, The Semantic Web -ISWC 2016 -15th International Semantic Web Conference, vol.9981, pp.498-514, 2016.
, DILIrank: the largest reference drug list ranked by the risk for developing drug-induced liver injury in humans, Drug Discov Today, vol.21, issue.4, pp.648-653, 2016.
, PARIS: probabilistic alignment of relations, instances, and schema, vol.5, pp.157-168, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00745191
, Feature selection in hierarchical feature spaces, Discovery Science -17th International Conference, vol.8777, pp.288-300, 2014.
, On the influence of description logics ontologies on conceptual similarity, Knowledge Engineering: Practice and Patterns, 16th International Conference, vol.5268, pp.48-63, 2008.
, A comparison of propositionalization strategies for creating features from linked open data, Proceedings of the 1st Workshop on Linked Data for Knowledge Discovery co-located with European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD 2014), vol.1232, 2014.
,
,
, T S 1,2,n such that {x, y, z} = {a 1 , b 1 , c n }
, Triangle-free graphs which are minimal for some nonstable 4-vertex subset, In Arab Journal of Mathematical Sciences, pp.159-169, 2015.
, 3-minimal triangle-free graphs, Discrete Mathematics, pp.3-8, 2014.
, Integer Partitions, 2004.
, Indecomposable tournaments and their indecomposable subtournaments on 5 and 7 vertices, Ars Combinatoria, pp.493-504, 2013.
, Les tournois (-1)-critiques, Communications in Mathematical Analysis, pp.83-97, 2007.
, les graphes (-1)-critiques, Ars combinatoria, pp.293-319, 2015.
, Finite tournaments with a nonempty diamond's support, Graphs and Combinatorics, pp.1653-1673, 2013.
, Tournaments whose indecomposability graph admits a vertex cover of size 2, Ars Combinatoria, pp.63-82, 2016.
, Prime critically and prime covering, In to apparent in journal Mathematical reports
, Description of the Triangle-free Prime Graphs Having at Most Two Non-Critical Vertices, Journal of Multi-Valued Logic and Soft Computing, pp.77-103, 2020.
, Indecomposability graph and critical vertices of an indecomposable graph, Discrete Math, pp.2839-2846, 2009.
, The 2-reconstructible indecomposable graphs, Comptes Rendus Mathematique, pp.1-4, 2007.
, Partially critical indecomposable graphs, Contributions to Discrete Mathematics, pp.40-59, 2008.
, Minimal indecomposable graphs, Discrete Math, pp.61-80, 1998.
, The Theory of 2-Structures. In A Framework for Decomposition and Transformation of Graphs, 1999.
, Primitivity is hereditary for 2-structures, Theoret. Comput. Sci, pp.343-358, 1990.
, The (?1)-critically duo-free tournaments, Ars Combinatoria, pp.391-402, 2005.
URL : https://hal.archives-ouvertes.fr/hal-02072360
, L'intervalle en théorie des relations, ses généralisations, filtre intervallaire et clô ture d'une relation, Order, Description and Roles, pp.313-342, 1984.
, Substitution des structures combinatoires, Théorie et Algorithmes, Thèse d'état, 1981.
, Indecomposable graphs, Discrete Math, pp.71-78, 1997.
, Comparability graphs, Graphs and Orders, pp.3-40, 1985.
, On minimal prime graphs and posets, Order, pp.357-375, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00863170
, Partially critical indecomposable tournaments and partially critical supports, Contributions to Discrete Mathematics, pp.52-76, 2011.
, Critically indecomposable partially ordered sets, graphs, tournaments and other binary relational structures, Discrete Math, pp.191-205, 1993.
, P 4-trees and substitution decomposition, In Discrete Appl. Math, pp.263-291, 1992.
, Graphs indecomposable with respect to the X-join, Discrete Math, pp.281-298, 1973.
, We say that a graph G is of order n and size m, if |V (G)| = n and |E(G)| = m. In this case, the graph G is called an (n, m)-graph. Given a graph G and X ? V , the subgraph of G induced by X is denoted by G[X]. A graph G is called a discrete graph if E(G) = ?. A graph G is called a path, denoted by P n , if it is of the form: V (P n ) = {v 1
, H is a star or H contains a cycle
, Leaf (H) ? Leaf (G), vol.4
, Definition 1 We call a B IO ? graph a bipartite indecomposable graph G of order n ? 5, with a bipartition {I
, 1: A B IO ? graph with 10 vertices
, Lemma 2.10 Let G be a B IO ? graph. Then G is unstable
, Note that if a graph G is indecomposable then G is connected since every nontrivial connected component is a nontrivial module of G. It follows that G ? e is decomposable when e is a bridge. Now, assume that e = xy ? N ob(G) is a non-bridge of G such that x ? O and y ? I. We denote d G (y) = n. Clearly, y is not a leaf of G and then n ? 2, G be a B IO ? graph and let e = xy be an edge of E(G)
, Lemma 2.11 Let G be a B IO ? graph and e = xy ? E(G) be a no proper bridge, such that x ? O and y ? I. Then, x ? Out(G) and either y ?
, By Definition 1, there exists a vertex v = y ? I such that v ? N G (x), which contradict the fact that x is a leaf. It follows that x ? Ins(G) ? Out(G)
, Lemma 2.12 Let G be a pendant graph. If G is unstable, then G is a B IO ? graph
, By Theorem 2.6, each cycle of G is of even length, and this is equivalent to say that G is bipartite. Second, let {I, O} be the bipartition of G and y ? I, with d G (y) = n. To conclude, we proceed by ? N G (y) and a vertices v i ? I such that N G (v i ) = X i . Now, consider e = xy ? E(G) and assume that d G (y) = n + 1. Since G is unstable and e ? N ob(G), then by Lemma 2.5, there exists a vertex v ? I
, Let G be an indecomposable graph. Assume that each pendant component H i , i ? 1, of G is either a
, First, assume that H i is an edge (E(H i ) = {e}). e ? N ob(G), Therefore, G ? e is disconnected, and thus, G ? e is decomposable. Otherwise, there exists i ? 1 such that e ? E(H i )
, Hence we may assume that G has at least two pendant components. Let H i be a pendant component of G. First, assume that |V (H i )| ? 4. Since H i has no proper bridges and G is triangle free by Theorem 2.3, then either H i C 4 or H i S p , with 2 ? p ? 4. Suppose that H i C 4 and let V (H i ) = {x 1 , x 2 , x 3 , x 4 } and E(H i ) = {x 1 x 2 , x 2 x 3
, Which contradicts the fact that G is indecomposable. Hence, we may assume that H i S p , with 2 ? p ? 4. By Lemma 2.9, we have Leaf (H i ) ? Leaf (G), then p = 2. Otherwise, G[Leaf (H i )] is a nontrivial module of G, which contradicts the fact that G is indecomposable. Consequently, H i is an edge. Second, assume that |V (H i )| ? 5. In this case, we will show that H i is a B IO ? graph. Using Lemma 2.12, it suffices to prove that H i is unstable (since H i is a pendant component of G). In a first step, we shall prove that H i is indecomposable. To the contrary, suppose that H i has a nontrivial module X. Since H i is triangle free and connected, By Lemma
, By Lemma 2.2, we have x is a leaf of H i , which is a contradiction. Consequently, H i is indecomposable. In a second step, we will show that H i has no removable edge. Consider an edge e = xy of H i . By definition of the pendant components, the first case, one can obviously observe that H i ? e is disconnected and then decomposable. In the second case, since G is unstable, by Lemma 2.5 it follows that G ? e has a unique discrete module of two vertices M e , say M e = {y, z}. Now it remains to prove that M e is a module of H i ? e. The vertex y ? M e is an inside vertex of G, and thus, by Lemma 2.1, it is not incident with a bridge of G. Then N G (y) ? V (H i ). Since M e is a module of G ? e, we have N G (z) = N G (y) \ {x}, and thus N G (M e ) ? V (H i )
, Consider an unstable graph G
, X p } on the vertex set of Out(C j ), such that: 1. for all i ? {1, . . . , p}, |X i | ? {2, 3}, 2. if |X i | = 2 there exists a vertex y ? Ins(C j ) such that X i ? N Cj (y), 3. if |X i | = 3 there exist two vertices y, z ? Ins(G) such that X i ? N Cj, vol.1
, We say that x is a representative vertex of G if x is incident with a proper bridge. We denote by R(G) = {x ? V (G)
, The graph G = G
, Given an unstable graph G of order n ? 4, consider C 1 , C 2 , . . . , C r , r ? 1, the family of it's pendant components such
, Consequently, G is a tree. Moreover, since G is an indecomposable graph, then G is a non-star tree
, Claim 2 If G is a pendant graph, then there exists a 2 ? placement ? such that ?(G) ? G 5
, Under this assumption, we will define a 2 ? placement ? on V (G) such that ?(G) ? G 5 . Let C i , 1 ? i ? r, be a pendant component of G and X i ? P(Out(C i ))
, 1: If |X i | = 2, say for instance that X i = {x i , y i } and we denote by u i , v i the respective neighbors leaves of x i , y i . First, we assume that |X i ? R(G)| = 0. In this case the permutation ? is defined on {x i , y i , u i , v i } by ?(x) = ? Ci (x). Second, assume that |X i ? R(G)| = 1. Without loss of generality
, In this case it suffices to consider the permutation ? defined on {x i , y i , u i , v i } by ?(x) = ? sp (x), p ? 2, if T S p (i.e T is isomorphic to S p ) with ? Sp is that given by Lemma 3.2 and Lemma 3.3 and ?(x) = ? U (x)
, We define a permutation ? on {x i , y i , u i , v i } by ?(x) = ? Sp (x) if x ? {x i , u i } and ?(x) = ? S p (x) if x ? {y i , v i }, Subcase.1.1: If, p.2
, We define a permutation ? on {x i , y i , u i , v i } as follows. First, if ? T (y i ) = y i , then ?(x) = ? Sp (x) if x ? {x i , u i }, ?(y i ) = ? T (y i ) and ?(v i ) = v i , with ? Sp is the permutation given by Lemma 3.2 and Lemma 3.3. Second, if ? T (y i ) = y i , then ?(x) = ? Sp (x), Subcase.1.2: If T S p , p ? 2, and Diam(T ) ? 3. By Theorem 1.4, there exists a permutation ? T defined on V (T ) such that ? T (T ) ? T 3
, Second if ? T (x i ) = x i and ? T (y i ) = y i (or ? T (x i ) = x i and ? T (y i ) = y i ), then ?(x) = ? U (x) with ? U is that given by Lemma 3.4. Finally, if ? T (x i ) = x i and ? T (y i ) = y i, Subcase.1.3: If Diam(T ) ? 3 and Diam(T ) ? 3. By Theorem 1.4, there exist permutations ? T , ? T defined respectively on V (T ) and V (T ) such that ? T (T ) ? T 3 and ? T (T ) ? T 3
, If |X i | = 3, assume that X i = {x i , y i , z i } and denote by u i , v i , w i the respective neighbors leaves of x i , y i , z i . First, assume that |X i ? R(G)| = 0
, In this case, if one of the trees T or T , say T , is isomorphic to S p , p ? 2, then it suffices to put ?(x) = ? Sp (x) for x ? {x i , u i } and identify ? with the permutations ? Sp , ? U defined by Lemmas 3.2, 3.3, 3.4 (When|X i | = 2), for x ? {y i , z i , v i , w i }. Otherwise, assume that Diam(T ) ? 3 and Diam(T ) ? 3. In this case, if ? T (x i ) = x i and ? T (y i ) = y i , then ?(x) = ? Ci (x) for x ? X i ? {u i , v i , w i }. Else, assume for instance that ? T (x i ) = x i . Then, it suffices to take ?(x i ) = ? T (x i ), ?(u i ) = u i and identify ? with the permutation ? U defined by Lemma 3.4 (Case.|X i | = 2), for x ? {y i , z i , v i , w i }. Finally, assume that |X i ? R(G)| = 3. Let T, T and T be the connected components of the representative graph G such that x i ? V (T ), y i ? V (T ) and z i ? V (T ). In this case, if one of the trees T, T or T , say for instance T , is isomorphic to S p , p ? 2, then it suffices to put ?(x) = ? Sp (x) for x ? {x i , u i }, and for x ? {y i , z i , v i, Then, either ?(x) = ? Sp (x) with ? Sp is that given by Lemma 3.2 and Lemma 3.3, or ?(x) = ? U (x) with ? U is that given by Lemma 3.4. Third, if |X i ? R(G)| = 2. Without loss of generalities, one can assume that x i , y i ? R(G)
, ) = x i , ? T (y i ) = y i and ? T (z i ) = z i . Then, we define a permutation ? on X i ? {u i , v i , w i } by ?(x i ) = ? T (x i ), ?(y i ) = ? T (y i ), ?(z i ) = ? T (z i ) and ?(x) = x for x ? {u i
, x i ) = x i , ? T (y i ) = y i . In this case, it suffices to put ?(x i ) = ? T (x i ), ?(u i ) = u i and for x ? {y i , z i , v i
, Packing of graphs and permutations-a survey, Discrete Mathematics, vol.276, issue.1, pp.379-391, 2004.
, Packing of graphs-a survey, Discrete Mathematics, vol.72, issue.1, pp.395-404, 1988.
, ) graphs in their complements, Israel Journal of Mathematics, vol.30, issue.4, pp.313-320, 1978.
, Embedding graphs in their complements, Czechoslovak Mathematical Journal, vol.31, issue.1, pp.53-62, 1981.
, A note on packing two trees into kn, Ars Combin, vol.11, pp.149-153, 1981.
, Packing two copies of a tree into its fourth power, Discrete Mathematics, vol.213, issue.1-3, pp.169-178, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00188438
, A note on embedding graphs without short cycles. Discrete mathematics, vol.286, pp.75-77, 2004.
, Packing two copies of a tree into its third power, Discrete Mathematics, vol.306, issue.21, pp.2779-2785, 2006.
, Given a digraph G = (V, E), to each nonempty subset X of V associate the subdigraph (X, E ? (X × X)) of G induced by X denoted by G X . With each digraph G = (V, E) associate its dual G * = (V, E * ) and its complement G = V, E defined as follows: Given x = y ? V, (x, y) ? E * if (y, x) ? E, and (x, y) ? E if (x, y) ? E. Two interesting types of digraphs are symmetric digraphs and tournaments. A digraph G = (V, E) is a symmetric digraph or graph (resp. tournament) whenever for x = y ? V, The theory of 2-structures: a framework for decomposition and transformation of graphs, 1999.
, a bijection f from V onto V is an isomorphism from G onto G provided that for any x, y ? V , (x, y) ? E if and only if (f (x), f (y)) ? E . The digraphs G and G are isomorphic, if there exists an isomorphism from one onto the other. Given two digraphs G and G on the same vertex set V . Let k be an integer with 0 < k < |V |, the digraphs G and G are k-hypomorphic if for every k-element subset X of V , the induced subdigraphs G X and G X are isomorphic. The digraphs G and G are (? k)-hypomorphic if they are t-hypomorphic for each integer t ? k. A digraph G is k-reconstructible if any digraph k-hypomorphic to G is isomorphic to G, Given two digraphs G =, 1970.
, They are hereditarily isomorphic up to complementation [2] if they are hereditarily isomorphic, or G and G are hereditarily isomorphic. Let k be a positive integer, the digraphs G and G are k-hypomorphic up to complementation (resp. k-hemimorphic) if for every k-element subset X of V , the induced subdigraphs G X and G X are isomorphic up to complementation (resp. hemimorphic). The digraphs G and G are (? k)-hypomorphic up to complementation (resp. (? k)-hemimorphic) if they are t-hypomorphic up to complementation (resp. t-hemimorphic) for each integer t ? k. A digraph G is k-reconstructible up to complementation, Given two digraphs G and G on the same vertex set V . They are hereditarily isomorphic, vol.25, pp.1-16, 2019.
, Hereditary hemimorphy of {?k}-hemimorphic tournaments for k ? 5, J. Korean Math. Soc, vol.48, issue.3, pp.599-626, 2011.
, La relation différence et l'anti-isomorphie, Math. Logic Quart, vol.41, issue.2, pp.268-280, 1995.
, Hypomorphy of graphs up to complementation, JCTB, Series B, vol.99, issue.1, pp.84-96, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00016564
, Boolean sum of graphs and reconstruction up to complementation, Advances in Pure and Applied Mathematics, vol.4, pp.315-349, 2013.
URL : https://hal.archives-ouvertes.fr/hal-02068014
, La demi-reconstructibilité des relations binaires d'au moins 13 éléments, C. R. Acad. Sci. Paris, t.317, Série I, pp.7-12, 1993.
, Un théorème de demi-reconstruction des relations binaires de cardinal >, vol.12, pp.1501643-1501644, 2017.
, Deux résultats concernant la détermination d'une relation par les types d'isomorphie de ses restrictions, C. R. Acad. Sci. Paris, t, vol.274, pp.1525-1528, 1972.
, Sur la détermination d'une relation par les types d'isomorphie de ses restrictions, C. R. Acad. Sci. Paris, t, vol.275, pp.951-953, 1972.
, Strongly self-complementary and hereditarily isomorphictournaments, Monatsh. Math, vol.81, issue.4, pp.291-304, 1976.
,
, S-metric space if for every u, v ? M it holds that d(u, v) ? S. A countable S-metric space M is a S-Urysohn metric space if it is homogeneous (that is, every isometry of its finite subspaces extends to an isometry from M to M) and every countable S-metric thus obtain: Corollary 2.1. Let S be a finite tight set of non-negative reals, Let S be a set of non-negative reals such that 0 ? S. A metric space M = (M, d) is
, This can be seen as a continuation of the research on (in)divisibility of metric spaces started by Delhommé, Laflamme, vol.10
, Recall that there is a up to isomorphism unique homogeneous triangle-free graph H (called the universal homogeneous triangle-free graph) such that every countable triangle-free graph embeds to H. We also obtain the first combinatorial proof of the following recent result by Dobrinen: Theorem 2.2 (Dobrinen 2020 [12]). The universal homogeneous triangle-free graph has finite big Ramsey degrees
, Ramsey's theorem for n-parameter sets, Transactions of the American Mathematical Society, vol.159, pp.257-292, 1971.
, A dual form of Ramsey's theorem, Advances in Mathematics, vol.53, issue.3, pp.265-290, 1984.
, A Ramsey theorem for trees, Journal of Combinatorial Theory, Series A, vol.26, issue.3, pp.215-237, 1979.
, Some partition theorems and ultrafilters on ?, 1979.
, Coloring subgraphs of the Rado graph, Combinatorica, vol.26, issue.2, pp.231-253, 2006.
, Pre-adjunctions and the Ramsey property, European Journal of Combinatorics, vol.70, pp.268-283, 2018.
, Distance sets of Urysohn metric spaces, Canadian Journal of Mathematics, vol.65, issue.1, pp.222-240, 2013.
, Divisibility of countable metric spaces, European Journal of Combinatorics, vol.28, issue.6, pp.1746-1769, 2007.
, Indivisible ultrametric spaces, Topology and its Applications, vol.155, issue.14, pp.1462-1478, 2008.
, Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups, European Journal of Combinatorics, vol.30, issue.4, pp.934-945, 2009.
, Structural Ramsey Theory of Metric Spaces and Topological Dynamics of Isometry Groups. Memoirs of the, 2010.
, The Ramsey theory of the universal homogeneous triangle-free graph, Journal of Mathematical Logic, p.2050012, 2020.
, The Ramsey theory of Henson graphs, 2019.
, A note on big Ramsey degrees, 2020.
, Big Ramsey degrees of 3-uniform hypergraphs, Acta Mathematica Universitatis Comenianae, vol.88, issue.3, pp.415-422, 2019.
, Simple permutations and pattern restricted permutations, Discrete Mathematics, vol.300, pp.1-15, 2005.
, Labelled induced subgraphs and well-quasi-ordering, Order, vol.32, issue.3, pp.313-328, 2015.
, Orbits of permutation groups on unordered sets, II. J. London Math. Soc, vol.23, issue.2, pp.249-264, 1981.
, Oligomorphic permutation groups, 1990.
, The algebra of an age, Model theory of groups and automorphism groups, pp.126-133, 1995.
, On an algebra related to orbit-counting, J. Group Theory, vol.1, issue.2, pp.173-179, 1998.
, On better quasi-ordering countable trees, Discrete Math, vol.53, pp.35-53, 1985.
, Well-partial orderings and hierarchies, Nederl. Akad. Wetensch. Proc. Ser. A 80=Indag. Math, vol.39, issue.3, pp.195-207, 1977.
, Representation of ideals of relational structures, Discrete Math, vol.309, issue.6, pp.1374-1384, 2009.
, Subgraphs and well-quasi-ordering, Journal of Graph Theory, vol.16, issue.5, pp.489-502, 1992.
, The theory of 2-structures. A framework for decomposition and transformation of graphs, 1999.
, Sur la comparaison des types de relations, C. R. Acad. Sci. Paris, vol.226, pp.987-988, 1948.
, Sur la comparaison des types d'ordres, C. R. Acad. Sci. Paris, vol.226, pp.1330-1331, 1948.
, Sur quelques classifications des systèmes de relations, Alger-Math, vol.1, pp.35-182, 1953.
, Sur l'extension aux relations de quelques propriétes des ordres, Ann. Sci. Ecole Norm. Sup, vol.71, pp.361-388, 1954.
, With an appendix by Norbert Sauer, Studies in Logic and the Foundations of Mathematics, vol.145, 2000.
, Quelques problèmes combinatoires concernant les ordres totaux et les relations monomorphes, Annales Institut Fourier Grenoble, vol.15, pp.415-524, 1965.
, A class of incidence matrices, Proc. Amer. Math. Soc, vol.17, pp.1233-1237, 1966.
, Transitiv orientbare graphen, Perfect graphs, vol.18, pp.25-66, 1967.
, Ordering by divisibility in abstract algebras, Proc. London Math. Soc, issue.3, pp.326-336, 1952.
, Contribution à l'étude des types d'ordres dispersés, pp.27-1968
, On incidence matrices of finite projective and affine spaces, Math. Z, vol.124, pp.315-318, 1972.
, Overview of general results in combinatorial enumeration, in Permutation patterns, London Math. Soc. Lecture Note Ser, vol.376, pp.3-40, 2010.
, Well-quasiordering depends on the labels, Acta Sci. Math. (Szeged), vol.55, issue.1-2, pp.59-65, 1991.
, The theory of well-quasi-ordering: a frequently discovered concept, J. Com. Th, vol.13, pp.297-305, 1972.
, Equimorphy-the case of chains, Archive for Mathematical Logic, vol.56, issue.7-8, pp.811-829, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02072148
, On Fraïssé's order type conjecture, Ann. of Math, issue.2, pp.89-111, 1971.
, An order type decomposition theorem, Ann. of Math, issue.2, pp.96-119, 1973.
, Growth rates in infinite graphs and permutation groups, J. London Math. Soc, vol.35, pp.276-286, 1987.
, Countable structures of a given age, The Journal of Symbolic Logic, vol.57, pp.992-1010, 1992.
, The metamathematics of algebraic systems, Studies in Logic and the Foundations of Mathematics, vol.66, pp.1936-1967, 1971.
, Foundations of bqo theory, Transactions of the A.M.S, vol.345, issue.2, pp.641-660, 1994.
, Excluded permutation matrices and the Stanley-Wilf conjecture, J. Combin. Theory, Ser. A, vol.107, pp.153-160, 2004.
, Basic wqo-and bqo-theory, Graphs and order, I.Rival Ed, pp.487-502, 1984.
, On well-quasi-ordering infinite trees, Proc, vol.61, pp.697-720, 1965.
, Sur l'énumération de structures discrètes: une approche par la théorie des relations, vol.249, p.pp, 2015.
, Profile and hereditary classes of relational structures, J. of MVLSC, vol.27, pp.475-500, 2016.
, Un belordre d'abritement et ses rapports avec les bornes d'une multirelation, Comptes rendus Acad. Sci. Paris, vol.274, pp.1677-1680, 1972.
, Application d'une propriété combinatoire des parties d'un ensemble aux groupes et aux relations, Math. Z, vol.150, pp.117-134, 1976.
, Sur la théorie des relations, 1978.
, The asymptotic behavior of a class of counting functions, Annals of Discrete Math, vol.79, pp.223-224, 1980.
, Applications of well quasi-ordering and better quasi-ordering, Graphs and order, pp.503-519, 1984.
, Sperner properties for groups and relations, Europ. J. Combinatorics, vol.7, pp.349-370, 1986.
, Sandwiches of ages, Ann. Pure Appl. Logic, vol.108, pp.295-326, 2001.
, Some relational structures with polynomial growth and their associated algebras I. Quasipolynomiality of the profile, The Electronic J. of Combinatorics, vol.20, issue.2, p.35, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01121195
, When is the orbit algebra of a group an integral domain? Proof of a conjecture of P, J. Cameron. Theor. Inform. Appl, vol.42, issue.1, pp.83-103, 2008.
, On a problem of formal logic, Proc. London Math. Soc, vol.30, pp.264-286, 1930.
, Graph minors. A survey, London Math. Soc. Lecture Note Ser, vol.103, pp.153-171, 1985.
, On the metamathematics of algebra, Studies in Logic and the Foundations of Mathematics, p.1951
, Pure and Applied Mathematics, vol.98, 1982.
, Well-partial orderings and their maximal order types. Habilitation, 1978.
, Sur les types d'ordre des ensembles linéaires, Fund. Math, vol.37, pp.253-264, 1950.
, Sur les âges de relations et quelques aspects homologiques des constructions D+M, 2002.
, On better quasi ordering countable series-parallel orders, Trans. Amer. Math Soc, vol.352, issue.6, pp.2491-2505, 1999.
, Chaînes d'idéaux et de sections initiales d'un ensemble ordonné, Publ. Dép. Math, issue.7, p.97, 1983.
, The profile of relations, Glob. J. Pure Appl. Math, vol.2, issue.3, pp.237-272, 2006.
, Overview of some general results in combinatorial enumeration, 2008.
, Hereditary properties of graphs: asymptotic enumeration, global structure, and colouring, Proceedings of the International Congress of Mathematicians, vol.III, pp.333-342, 1998.
, Hereditary properties of combinatorial structures: posets and oriented graphs, J. Graph Theory, vol.56, issue.4, pp.311-332, 2007.
, The unlabelled speed of a hereditary graph property, J. Combin. Theory Ser. B, vol.99, issue.1, pp.9-19, 2009.
, Excluded permutation matrices and the Stanley-Wilf conjecture, J. Combin. Theory Ser. A, vol.107, issue.1, pp.153-160, 2004.
, Simple permutations and pattern restricted permutations, Discrete Math, vol.300, issue.1-3, pp.1-15, 2005.
, Permutation classes of polynomial growth, Ann. Comb, vol.11, issue.3-4, pp.249-264, 2007.
, Small permutation classes, Proceedings of the London Mathematical Society, vol.103, issue.5, pp.879-921, 2011.
, On growth rates of closed permutation classes, Electron. J. Combin, vol.9, issue.2, 2003.
, On growth rates of permutations, set partitions, ordered graphs and other objects, Electron. J. Combin, vol.15, issue.1, 2008.
, Decomposing simple permutations, with enumerative consequences, Combinatorica, vol.28, issue.4, pp.385-400, 2008.
, Profile and hereditary classes of relational structures, Proceedings ISOR'11, International Symposium on Operational Research, 2011.
, Oligomorphic permutation groups, London Mathematical Society Lecture Note Series, vol.152, 1990.
, Oligomorphic permutation groups, Perspectives in Mathematical Sciences II: Pure Mathematics, pp.37-61, 2009.
, The asymptotic behavior of a class of counting functions, Combinatorics 79. Part II, Proceedings of the Colloquium, vol.9, pp.223-224, 1979.
, Application de la notion de relation presque-enchaînable au dénombrement des restrictions finies d'une relation, Z. Math. Logik Grundlag. Math, vol.27, issue.4, pp.289-332, 1981.
, Some relational structures with polynomial growth and their associated algebras I: Quasi-polynomiality of the profile, Electron. J. Combin, vol.20, issue.2, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01121195
, The morphology of infinite tournaments; application to the growth of their profile, European J. Combin, vol.31, issue.2, pp.461-481, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00853566
, Classification of P-oligomorphic groups, conjectures of Cameron and Macpherson, 2020.
URL : https://hal.archives-ouvertes.fr/tel-02420262
,
, Triangle-free graphs which are minimal for some nonstable 4-vertex subset, Arab J. Math. Sc, vol.21, issue.2, pp.159-169, 2015.
, 3-minimal triangle-free graphs, Discrete Math, vol.331, pp.3-8, 2014.
, Cut-primitive directed graphs versus clan-primitive directed graphs, Adv. Pure Appl. Math, vol.1, pp.223-231, 2010.
, Minimal indecomposable graphs, Discrete Math, vol.183, pp.61-80, 1998.
, The Theory of 2-Structures. A Framework for Decomposition and Transformation of Graphs, 1999.
, Primitivity is hereditary for 2-structures, fundamental study, Theoret. Comput. Sci, vol.3, issue.70, pp.343-358, 1990.
, Acta Math. Acad. Sci. Hungar, vol.18, pp.25-66, 1967.
, A translation of Tibor Gallai's paper: Transitiv orientierbare Graphen, In: Perfect graphs, pp.25-66, 2001.
, Introduction to Graph Theory, 2001.
, Notes about the carathéodory number, Discret. Comput. Geom, vol.48, issue.3, pp.783-792, 2012.
, ? k)-reconstructible binary relations, Eur. J. Comb, vol.37, pp.43-67, 2014.
, The minimal non (? k)-reconstructible relations, Discr. Math, vol.291, pp.19-40, 2005.
, The modular decomposition of countable graphs. Definition and construction in monadic second-order logic, Theor. Comp. Sc, vol.394, issue.2, pp.1-38, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00353765
, Abritement entre relations et spécialement entre chaînes, Instituto Nazionale di Alta Mathematica, vol.5, pp.203-251, 1970.
, Transitiv orientierbare Graphen. Acta math. Acad. Sci. Hungar, vol.18, pp.25-66, 1967.
, Caractérisation des classes de (? 3)-hypomorphie à l'aide d'interdits, Proyecciones Journal of Mathematics, vol.32, issue.2, pp.91-105, 2013.
, Decomposition of infinite labeled 2-structures, Lec. N. Cmp. Sc, vol.812, pp.145-158, 1994.
, L'indéformabilité des relations et multirelations binaires, Z. Math. Logik Grundlag. Math, vol.24, pp.303-317, 1978.
, Reconstruction of binary relations from their restrictions of cardinality 2, 3, 4 and n ? 1. I, Z. Math. Log. Grundl. Math, vol.38, pp.27-37, 1992.
, Combinatorics of finite sets, 1987.
, When is a quotient of the Boolean lattice a symmetric chain order?, 2006.
, Inequalities for subsets of a set and KLYM posets, SIAM J. Alg. Disc. Meth, vol.4, pp.67-69, 1983.
, The width of downsets, Europ. J. Combinatorics, vol.79, pp.46-59, 2019.
, Covers of convex subsets of distributive lattices by intervals
, Symmetric chain decompositions of quotients by wreath products, Electronic J. Combin, vol.22, issue.2, 2015.
, , 2015.
, Strong versions of Sperner's theorem, J. Combin. Theory Ser. A, vol.20, pp.80-88, 1976.
, Sperner properties of the ideals of a Boolean lattice, 2009.
, Application d'une proprieté combinatoire des parties d'un ensemble aux groupes and aux relations, Math Z, vol.150, pp.117-134, 1976.
, Sperner properties for groups and relations, Europ. J. Combinatorics, vol.7, pp.349-370, 1986.
, Iterated arc graphs, Comment. Math. Univ. Carolin, vol.59, pp.277-283, 2018.
, Weyl groups, the hard Lefschetz theorem, and the Sperner property, SIAM J. Alg. Disc. Meth, vol.1, pp.168-184, 1980.
, Some aspects of groups acting on finite posets, J. Combinatorial Theory A, vol.32, pp.132-161, 1982.
, Quotients of Peck posets, Order, vol.1, pp.29-34, 1984.
, A remark on minimal polynomials of Boolean functions
, A symmetric chain decomposition of L(n, 4), European J. Combin, vol.1, pp.379-383, 1980.
, ON LOGICS THAT MAKE A BRIDGE FROM THE DISCRETE TO THE
, Chain logic and shelah's infinitary logic, 2019.
, Large networks and graph limits, vol.60, 2012.
, Languages with expressions of infinite length, 1959.
, First-order limits, an analytical perspective, European J. Combin, vol.52, pp.368-388, 2016.
, LDFS-based certifying algorithm for the minimum path cover problem on cocomparability graphs, SIAM J. Comput, vol.42, issue.3, pp.792-807, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00936300
, A new LBFS-based algorithm for cocomparability graph recognition, Discrete Applied Mathematics, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01274023
, Between O(nm) and O(n alpha ), SIAM J. Comput, vol.36, issue.2, pp.310-325, 2006.
, Revisiting decomposition by clique separators, SIAM J. Discrete Math, vol.32, issue.1, pp.682-694, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01753324
, Maximal cliques structure for cocomparability graphs and applications, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01393927
, Algorithmic Graph Theory and Perfect Graphs, Annals of Discrete Mathematics, vol.57, 2004.
, Algorithmic aspects of comparability graphs and interval graphs, NATO ASI Series, vol.147, pp.41-101, 1985.
, Graph Classes, a survey. SIAM Monographs on Discrete Mathematics and Applications, 1999.
, Domination on cocomparability graphs, SIAM J. Discrete Math, vol.6, issue.3, pp.400-417, 1993.
, A linear-time algorithm for maximum-cardinality matching on cocomparability graphs, SIAM J. Discret. Math, vol.32, issue.4, pp.2820-2835, 2018.
, On the power of graph searching for cocomparability graphs, SIAM J. Discrete Math, vol.30, issue.1, pp.569-591, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01273687
, Triangulating graphs without asteroidal triples, Discrete Appl. Math, vol.64, issue.3, pp.281-287, 1996.
, Recognition and computation of minimal triangulations for AT-free claw-free and co-comparability graphs, Discrete Applied Mathematics, vol.146, issue.3, pp.193-218, 2005.
, A unified view of graph searching, SIAM J. Discrete Math, vol.22, issue.4, pp.1259-1276, 2008.
, Asymptotic Differential Algebra and Model Theory of Transseries. Number 195 in Annals of Mathematics studies, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02350411
, On numbers, germs, and transseries, Proc. Int, vol.1, pp.1-24, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02350415
, The surreal numbers as a universal H-field, J. Eur. Math. Soc, vol.21, issue.4, pp.1179-1199, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02350421
, Surreal numbers, derivations and transseries, JEMS, vol.20, issue.2, pp.339-390, 2018.
, Fonctions d'une variable réelle, Éléments de Mathématiques (Chap. 5). Hermann, 2-nd edition, 1961.
, Sur les fondements de la théorie des ensembles transfinis, Jacques Gabay, 1899. Reprint from les Mémoires de la Société des Sciences physiques et naturelles de
, On numbers and games, 1976.
, Notes on exponential-logarithmic terms, Fundamenta Mathematicae, vol.127, pp.45-50, 1986.
, Über asymptotische Werte, infinitäre Approximationen und infinitäre Auflösung von Gleichungen, Math. Ann, vol.8, pp.363-414, 1875.
, Über die Paradoxen des Infinitärscalcüls, Math. Ann, vol.11, pp.149-167, 1877.
, Introduction aux fonctions analysables et preuve constructive de la conjecture de Dulac. Hermann, collection: Actualités mathématiques, 1992.
, The rise of non-Archimedean mathematics and the roots of a misconception i: the emergence of non-Archimedean systems of magnitudes, Arch. Hist. Exact Sci, vol.60, pp.1-121, 2006.
, An Introduction to the Theory of Surreal Numbers, 1986.
, Orders of infinity, 1910.
, Properties of logarithmico-exponential functions, Proceedings of the London Mathematical Society, vol.10, issue.2, pp.54-90, 1911.
, Grundzüge einer Theorie der geordneten Mengen, Math. Ann, vol.65, pp.435-505, 1908.
, Automatic asymptotics, 1997.
, Transseries and real differential algebra, Lecture Notes in Mathematics, vol.1888, 2006.
, Surreal Numbers: How Two Ex-students Turned on to Pure Mathematics and Found Total Happiness : a Mathematical Novelette, 1974.
, If R is finite, there is just one sibling. The famous Cantor-Bernstein-Schroeder Theorem states that this is the case even for infinite sets, structures in a language with pure equality: if there is an injection from one set to another and vice-versa, then there is a bijection between these two sets. The same situation occurs in other (categorical) structures such as vectors spaces, A sibling of a given (relational) structure R is any structure S which can be embedded into R, and vice versa
, R) be the number of siblings of R (in its category), these siblings being counted up to isomorphism
, The first one is the Bonato -Tardif conjecture, often referred to as the Tree Alternative Conjecture
, Here, trees are connected (undirected) graphs without any cycle. Bonato and Tardif proved that the conjecture holds for rayless trees
, Tyomkyn proved that the tree alternative property for rooted trees, 2009.
, ? 0 for every locally finite tree T having a non-surjective embedding, except only for the infinite path
, Sprüssel Twins of rayless graphs, J. Combin. Theory Ser. B, vol.101, issue.1, pp.60-65, 2011.
, Mutually embeddable graphs and the tree alternative conjecture, J. Combin. Theory Ser, issue.96, pp.874-880, 2006.
, Fixed configurations in graphs with small number of disjoint rays, Contemporary Methods in Graph Theory, pp.639-649, 1990.
, Macpherson Relational structures determined by their finite induced substructures, J. Symbolic Logic, vol.53, issue.1, pp.222-230, 1988.
, Sauer Invariant subsets of scattered trees and the tree alternative property of Bonato and Tardif, In Abh. Math. Semin. Univ. Hambg, vol.87, issue.2, pp.369-408, 2017.
, Siblings of an ? 0 -categorical relational structure, Proceedings of the BIRS conference on Homegenous Structures, 2015.
URL : https://hal.archives-ouvertes.fr/hal-02071530
, Equimorphy: the case of chains, In Arch. Math. Logic, vol.56, issue.7-8, pp.811-829, 2017.
URL : https://hal.archives-ouvertes.fr/hal-02072148
, Conjectures on Countable Relations Circulating manuscript, p.17, 2000.
, APPLICATIONS OF ORDER TREES IN INFINITE GRAPHS Given an order tree (T, ?), we say that a graph G = (V, E) is a T -graph if V =, Discrete Math, vol.309, pp.5963-5967, 2009.
, Not all graphs admit a normal tree order (consider an uncountable clique where every edge has been subdivided once) and it is an open problem to characterise the graphs which do. Much more is known about which graphs admit a normal tree order (T, ?) where (T, ?) is a graph-theoretic tree (i.e. an order tree of height at most ?). In this case, T is called a normal spanning tree of G. This concept is due to Jung [2], who also offered a first characterization of graphs admitting a normal spanning tree, G is (isomorphic to) a T -graph for some order tree (T, ?), we say that
, From Halin's conjecture, one obtains a forbidden minor characterization of the graphs admitting a normal spanning tree. Diestel and Leader have asked to classify the minor-minimal forbidden graphs in this list, vol.5
, Classify the minor-minimal forbidden graphs for the property of having a normal spanning tree up to minor-equivalence
, Generalising the constructions of Thomas and Komjath that uncountable graphs are not well-quasi-ordered under the
, An end of a graph G is an equivalence class of rays, where two rays R and S of G are equivalent if and only if there are infinitely many vertex disjoint paths between R and S in G. The degree deg(?) of an end ? is the maximum cardinality of a collection of pairwise disjoint rays in ?
, Given a family R = (R i : i ? I)
, Halin's conjecture is trivially true for ends of finite degree, and has been proven by Halin himself for ends of countable degree (the so-called Halin's grid theorem)
, HC(? 1 ) fails, HC(? n ) holds for all 2 ? n ? ?, HC(? ?+1 ) fails again, and HC(? ?+n ) for n ? N with n ? 2 is undecidable in ZFC. I will give an impression of our counterexamples which are built on certain T -graphs -in the case of HC(? 1 ) on a certain Aronszajn tree T , and in the case of HC, Recently, we have clarified the truth of HC(?) for the first cardinals as follows
, Normal tree orders for infinite graphs, Transactions of the American Mathematical Society, vol.345, issue.2, pp.871-895, 1994.
, Wurzelbäume und unendliche Wege in Graphen, Mathematische Nachrichten, vol.41, issue.1-3, pp.1-22, 1969.
, Miscellaneous problems on infinite graphs, Journal of Graph Theory, vol.35, issue.2, pp.128-151, 2000.
, Proof of Halin's normal spanning tree conjecture, 2020.
, Normal spanning trees, Aronszajn trees and excluded minors, Journal of the London Mathematical Society, vol.63, pp.16-32, 2001.
, A new obstruction for normal spanning trees, 2020.
, A note on minor antichains of uncountable graphs, 2020.
, On ?-discreteness and borel isomorphism, American Journal of Mathematics, vol.85, issue.4, pp.655-666, 1963.
, Über die Maximalzahl fremder unendlicher Wege in Graphen, Mathematische Nachrichten, vol.30, issue.1-2, pp.63-85, 1965.
, Halin's ray graph conjecture
, Zélus, a Synchronous Language with ODEs, International Conference on Hybrid Systems: Computation and Control (HSCC 2013), 2013.
, A Type-based Analysis of Causality Loops in Hybrid Systems Modelers, International Conference on Hybrid Systems: Computation and Control (HSCC), 2014.
URL : https://hal.archives-ouvertes.fr/hal-01549183
, A Formally Verified Compiler for Lustre, International Conference on Programming Language, Design and Implementation (PLDI), 2017.
URL : https://hal.archives-ouvertes.fr/hal-01512286
, Mechanized Semantics and Verified Compilation for a Dataflow Synchronous Language with Reset, International Conference on Principles of Programming Languages (POPL), 2020.
URL : https://hal.archives-ouvertes.fr/hal-02426573
, Studies in Logic and the Foundations of Mathematics, vol.145, 2000.
, Cameron Oligomorphic Permutation Groups, In London Math. Soc. Lecture Notes, vol.152, 1990.
, The poset of copies for automorphism groups of countable relational structures. Submitted to the Rosenberg Special Issue
URL : https://hal.archives-ouvertes.fr/hal-02512435
, Norbert Sauer Colouring homogeneous structures
, Jaroslav Ne?et?il All those Ramsey classes, 2016.
, Siblings of an ? 0 -categorical relational structure, Lionel Nguyen Van Thé. It is available on arXiv
URL : https://hal.archives-ouvertes.fr/hal-02071530
, Ehud Hrushovski Extending partial isomorphisms of graphs, In Combinatorica, vol.12, issue.4, pp.411-416, 1992.
, Andy Zucker Big Ramsey degrees and topological dynamics, Groups, pp.235-276, 2018.
, Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups, Geometric and Functional Analysis, vol.15, pp.106-189, 2005.
, Urysohn Sphere is oscillation stable, Goemetric and Functional Analysis, vol.19, pp.536-557, 2009.
, Ward Henson Countable homogeneous relational structures and ? 0 -categorical theories, In Journal of Symbolic Logic, vol.3, issue.37, pp.494-500, 1972.
, Vojt?ch Rödl Coloring of universal graphs, Graphs and Combinatorics, vol.2, pp.55-60, 1986.
, Norbert Sauer Coloring subgraphs of the Rado graph, Combinatorica, vol.26, pp.231-253, 2006.
, Natasha Dobrinen The Ramsey theory of Henson graphs, 2019.
, Denis Devlin Some partition theorems and ultrafilters on ?, PhD thesis, 1979.
, The class of graphs with twin-width at most d is small, i.e. there are c n .n! such labeled graphs on the vertex set 1
, one can immediately derives that cubic graphs have unbounded twin-width. However, there are some (Bilu-Linial) cubic expanders with twin width at most 6, hence even for cubic graphs, the separation bounded/unbounded twin-width is unclear