H. Aboueisha, S. Hussain, V. Lozin, J. Monnot, and B. Ries, A Dichotomy for Upper Domination in Monogenic Classes, Du. Lecture Notes in Computer Science, vol.8881, issue.101, pp.258-267, 2014.
DOI : 10.1007/978-3-319-12691-3_20
URL : https://hal.archives-ouvertes.fr/hal-01434163

R. Aharoni, Ryser's Conjecture for Tripartite 3-Graphs, Combinatorica, vol.21, issue.1, pp.1-4, 2001.
DOI : 10.1007/s004930170001

J. Akiyama and M. Kano, Factors and Factorizations of Graphs, Lecture Notes in Mathematics, vol.2031, 2011.
DOI : 10.1007/978-3-642-21919-1

T. Akiyama, T. Nishizeki, and N. Saito, NP-Completeness of the Hamiltonian Cycle Problem for Bipartite Graphs, In: Journal of Information Processing, vol.3, issue.116, pp.73-76, 1980.

V. E. Alekseev, On easy and hard hereditary classes of graphs with respect to the independent set problem, Discrete Applied Mathematics, vol.132, issue.1-3, pp.17-26, 2003.
DOI : 10.1016/S0166-218X(03)00387-1

V. E. Alekseev and D. S. Malyshev, A criterion for a class of graphs to be a boundary class and applications, Russian), pp.3-10, 2008.

V. E. Alekseev, D. V. Korobitsyn, and V. V. Lozin, Boundary classes of graphs for the dominating set problem, Discrete Mathematics, vol.285, issue.1-3, pp.1-3, 2004.
DOI : 10.1016/j.disc.2004.04.010

V. E. Alekseev, R. Boliac, D. V. Korobitsyn, and V. V. Lozin, NP-hard graph problems and boundary classes of graphs, Theoretical Computer Science, vol.389, issue.1-2, pp.219-236, 2007.
DOI : 10.1016/j.tcs.2007.09.013
URL : https://doi.org/10.1016/j.tcs.2007.09.013

P. Anand, H. Escuadro, R. Gera, S. G. Hartke, and D. Stolee, On the hardness of recognizing triangular line graphs, Discrete Mathematics, vol.312, issue.17, pp.2627-2638, 2012.
DOI : 10.1016/j.disc.2011.11.037

V. Andova, F. Kardo?, and R. ?krekovski, Mathematical aspects of fullerenes, In: Ars Mathematica Contemporanea, vol.11, issue.2, pp.353-379, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01416354

R. P. Anstee, A Survey of Forbidden Configuration Results, In: Electronic Journal of Combinatorics, vol.20, 2013.

M. Anthony, G. Brightwell, and C. Cooper, The vapnik-chervonenkis dimension of a random graph, Discrete Mathematics, vol.138, issue.1-3, pp.43-56, 1995.
DOI : 10.1016/0012-365X(94)00187-N

E. M. Arkin, S. P. Fekete, K. Islam, H. Meijer, J. S. Mitchell et al., Not being (super)thin or solid is hard: A study of grid Hamiltonicity, Computational Geometry, vol.42, issue.6-7, pp.582-605, 2009.
DOI : 10.1016/j.comgeo.2008.11.004

S. Arnborg, J. Lagergren, and D. Seese, Easy problems for tree-decomposable graphs, Journal of Algorithms, vol.12, issue.2, pp.308-340, 1991.
DOI : 10.1016/0196-6774(91)90006-K
URL : http://www.aifb.uni-karlsruhe.de/CoM/seese/publications/../../publications/tree-decomposable_graphs.pdf

S. Arora and B. Barak, Computational Complexity -A Modern Approach, 2009.
DOI : 10.1017/cbo9780511804090

L. Babai and P. Frankl, Linear Algebra Method in Combinatorics. Preliminary Version 2, 1992.

V. Bafna, P. Berman, and T. Fujito, A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem, SIAM Journal on Discrete Mathematics, vol.12, issue.3, pp.289-297, 1999.
DOI : 10.1137/S0895480196305124

B. S. Baker, Approximation algorithms for NP-complete problems on planar graphs, Journal of the ACM, vol.41, issue.1, pp.153-180, 1994.
DOI : 10.1145/174644.174650

L. W. Beineke, Characterizations of derived graphs, Journal of Combinatorial Theory, vol.9, issue.2, pp.129-135, 1970.
DOI : 10.1016/S0021-9800(70)80019-9
URL : https://doi.org/10.1016/s0021-9800(70)80019-9

L. W. Beineke and R. J. Wilson, Topics in Topological Graph Theory, 2009.
DOI : 10.1017/CBO9781139087223

P. Berman and M. Karpinski, Efficient Amplifiers and Bounded Degree Optimization, Electronic Colloquium on Computational Complexity, 2003.

P. Berman and M. Karpinski, Improved Approximation Lower Bounds on Small Occurrence Optimization, Electronic Colloquium on Computational Complexity, 2003.

A. A. Bertossi, The edge Hamiltonian path problem is NP-complete, Information Processing Letters, vol.13, issue.4-5, pp.4-5, 1981.
DOI : 10.1016/0020-0190(81)90048-X

T. Biedl, E. D. Demaine, C. A. Duncan, R. Fleischer, and S. G. Kobourov, Tight bounds on maximal and maximum matchings, In: Discrete Mathematics, vol.285, pp.1-3, 2004.
DOI : 10.1016/j.disc.2004.05.003
URL : https://doi.org/10.1016/j.disc.2004.05.003

H. L. Bodlaender, A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth, SIAM Journal on Computing, vol.25, issue.6, pp.1305-1317, 1996.
DOI : 10.1137/S0097539793251219

H. L. Bodlaender, A partial k-arboretum of graphs with bounded treewidth, Theoretical Computer Science, vol.209, issue.1-2, pp.1-45, 1998.
DOI : 10.1016/S0304-3975(97)00228-4

H. L. Bodlaender, Planar Graphs With Bounded Treewidth. Tech. rep. RUU-CS-88-14, Rijksuniversiteit Utrecht, p.61, 1988.

J. A. Bondy and U. S. Murty, Graph Theory. Graduate Texts in Mathematics, 2008.

A. Brandstädt, (P5,diamond)-free graphs revisited: structure and linear time optimization, Discrete Applied Mathematics, vol.138, issue.1-2, pp.1-2, 2004.
DOI : 10.1016/S0166-218X(03)00266-X

H. Brönnimann and M. T. Goodrich, Almost optimal set covers in finite VC-dimension, Discrete & Computational Geometry, vol.16, issue.2, pp.463-479, 1995.
DOI : 10.1145/73393.73397

M. R. Cerioli, L. Faria, T. O. Ferreira, C. A. Martinhon, F. Protti et al., Partition into cliques for cubic graphs: Planar case, complexity and approximation, Discrete Applied Mathematics, vol.156, issue.12, pp.2270-2278, 2008.
DOI : 10.1016/j.dam.2007.10.015
URL : https://doi.org/10.1016/j.dam.2007.10.015

G. Chappell, J. Gimbel, and C. Hartman, On cycle packings and feedback vertex sets, In: Contributions to Discrete Mathematics, vol.9, issue.2, pp.48-74, 2014.

G. Chapuy, M. Devos, J. Mcdonald, B. Mohar, and D. Scheide, Packing Triangles in Weighted Graphs, SIAM Journal on Discrete Mathematics, vol.28, issue.1, pp.226-239, 2014.
DOI : 10.1137/100803869
URL : https://hal.archives-ouvertes.fr/hal-01185317

G. Chartrand, On hamiltonian line-graphs, Transactions of the American Mathematical Society, vol.134, issue.3, pp.559-566, 1968.
DOI : 10.1090/S0002-9947-1968-0231740-1

G. Chartrand, The existence of complete cycles in repeated line-graphs, Bulletin of the American Mathematical Society, vol.71, issue.4, pp.668-670, 1965.
DOI : 10.1090/S0002-9904-1965-11389-1

H. B. Chen, H. L. Fu, and C. H. Shih, FEEDBACK VERTEX SET ON PLANAR GRAPHS, Taiwanese Journal of Mathematics, vol.16, issue.6, pp.2077-2082, 2012.
DOI : 10.11650/twjm/1500406840

M. Chlebík and J. Chlebíková, Complexity of approximating bounded variants of optimization problems, Theoretical Computer Science, vol.354, issue.3, pp.320-338, 2006.
DOI : 10.1016/j.tcs.2005.11.029

M. Chlebík and J. Chlebíková, ???Dimensional Boxes, SIAM Journal on Discrete Mathematics, vol.21, issue.1, pp.158-169, 2007.
DOI : 10.1137/050629276

S. A. Choudum, T. Karthick, and M. A. Shalu, Linear Chromatic Bounds for a Subfamily of 3K 1-free Graphs, Graphs and Combinatorics, vol.24, issue.5, pp.413-428, 2008.
DOI : 10.1007/s00373-008-0801-0

M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:msub><mml:mi>K</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>-free graphs with no odd holes, Journal of Combinatorial Theory, Series B, vol.100, issue.3, pp.313-331, 2010.
DOI : 10.1016/j.jctb.2009.10.001

M. Chudnovsky, N. Robertson, P. Seymour, and R. Thomas, The strong perfect graph theorem, Annals of Mathematics, vol.164, issue.1, pp.51-229, 2006.
DOI : 10.4007/annals.2006.164.51
URL : http://annals.math.princeton.edu/wp-content/uploads/annals-v164-n1-p02.pdf

V. Chvátal and P. L. Hammer, Aggregation of Inequalities in Integer Programming, Nemhauser. Annals of Discrete Mathematics, vol.1, pp.145-162, 1977.
DOI : 10.1016/S0167-5060(08)70731-3

M. Conforti, D. G. Corneil, and A. R. Mahjoub, Ki-covers I: Complexity and polytopes, Discrete Mathematics, vol.58, issue.2, pp.121-142, 1986.
DOI : 10.1016/0012-365X(86)90156-1
URL : https://doi.org/10.1016/0012-365x(86)90156-1

M. Conforti, D. C. Corneil, and A. R. Mahjoub, Ki-covers. II.Ki-perfect graphs, Journal of Graph Theory, vol.54, issue.4, pp.569-584, 1987.
DOI : 10.1002/jgt.3190110415

C. R. Cook, Two characterizations of interchange graphs of complete m-partite graphs, Discrete Mathematics, vol.8, issue.4, pp.305-311, 1974.
DOI : 10.1016/0012-365X(74)90150-2

B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Information and Computation, vol.85, issue.1, pp.12-75, 1990.
DOI : 10.1016/0890-5401(90)90043-H
URL : https://hal.archives-ouvertes.fr/hal-00353765

B. Courcelle and S. Olariu, Upper bounds to the clique width of graphs, Discrete Applied Mathematics, vol.101, issue.1-3, pp.77-114, 2000.
DOI : 10.1016/S0166-218X(99)00184-5

B. Courcelle, J. Engelfriet, and G. Rozenberg, Handle-rewriting hypergraph grammars, Journal of Computer and System Sciences, vol.46, issue.2, pp.218-270, 1993.
DOI : 10.1016/0022-0000(93)90004-G
URL : https://doi.org/10.1016/0022-0000(93)90004-g

B. Courcelle, J. A. Makowsky, and U. Rotics, Linear Time Solvable Optimization Problems on Graphs of Bounded Clique-Width, Theory of Computing Systems, vol.33, issue.2, pp.125-150, 2000.
DOI : 10.1007/s002249910009

E. D. Demaine and M. T. Hajiaghayi, The Bidimensionality Theory and Its Algorithmic Applications, The Computer Journal, vol.51, issue.3, 2007.
DOI : 10.1093/comjnl/bxm033

R. W. Deming, Independence numbers of graphs-an extension of the Koenig-Egervary theorem, Discrete Mathematics, vol.27, issue.1, pp.23-33, 1979.
DOI : 10.1016/0012-365X(79)90066-9

R. J. Douglas, NP-completeness and degree restricted spanning trees, Discrete Mathematics, vol.105, issue.1-3, pp.41-47, 1992.
DOI : 10.1016/0012-365X(92)90130-8
URL : https://doi.org/10.1016/0012-365x(92)90130-8

T. Do?li´cdo?li´c, Cyclical Edge-Connectivity of Fullerene Graphs and (k, 6)-Cages, Journal of Mathematical Chemistry, vol.33, issue.2, pp.103-112, 2003.
DOI : 10.1023/A:1023299815308

D. Du, K. Ko, and X. Hu, Design and Analysis of Approximation Algorithms . Springer Optimization and Its Applications, p.2012
DOI : 10.1007/978-1-4614-1701-9

P. Duchet and H. Meyniel, On Hadwiger's Number and the Stability Number, In: Ann. Discr. Math, vol.13, pp.71-74, 1982.
DOI : 10.1016/S0304-0208(08)73549-7

M. N. Ellingham and J. D. Horton, Non-hamiltonian 3-connected cubic bipartite graphs, Journal of Combinatorial Theory, Series B, vol.34, issue.3, pp.350-353, 1983.
DOI : 10.1016/0095-8956(83)90046-1
URL : https://doi.org/10.1016/0095-8956(83)90046-1

P. Erd?-os, Graph theory and probability, Journal canadien de math??matiques, vol.11, issue.0, pp.34-38, 1959.
DOI : 10.4153/CJM-1959-003-9

P. Erd?-os and L. Pósa, On independent circuits contained in a graph, Journal canadien de math??matiques, vol.17, issue.0, pp.347-352, 1965.
DOI : 10.4153/CJM-1965-035-8

B. Escoffier, L. Gourvès, and J. Monnot, Complexity and approximation results for the connected vertex cover problem in graphs and hypergraphs, Journal of Discrete Algorithms, vol.8, issue.1, pp.36-49, 2010.
DOI : 10.1016/j.jda.2009.01.005
URL : https://hal.archives-ouvertes.fr/hal-00178912

S. Fajtlowicz, Independence, clique size and maximum degree, Combinatorica, vol.1, issue.2, pp.35-38, 1984.
DOI : 10.1007/BF02579154

S. Fajtlowicz, On the size of independent sets in graphs, In: Congressus Numerantium, vol.21, pp.269-274, 1978.

H. Fernau and D. F. Manlove, Vertex and edge covers with clustering properties: Complexity and algorithms, Journal of Discrete Algorithms, vol.7, issue.2, pp.149-167, 2009.
DOI : 10.1016/j.jda.2008.09.007
URL : https://doi.org/10.1016/j.jda.2008.09.007

F. V. Fomin and D. Kratsch, Exact Exponential Algorithms. Texts in Theoretical Computer Science. An EATCS Series, 2010.
DOI : 10.1007/978-3-642-16533-7
URL : https://hal.archives-ouvertes.fr/hal-00085561

P. Frankl and J. Pach, On the Number of Sets in a Null t-Design, European Journal of Combinatorics, vol.4, issue.1, pp.21-23, 1983.
DOI : 10.1016/S0195-6698(83)80004-3

K. Fraughnaugh and S. C. Locke, 11/30 (Finding Large Independent Sets in Connected Triangle-Free 3-Regular Graphs), Journal of Combinatorial Theory, Series B, vol.65, issue.1, pp.51-72, 1995.
DOI : 10.1006/jctb.1995.1043
URL : https://doi.org/10.1006/jctb.1995.1043

K. and F. Jones, Independence in graphs with maximum degree four, Journal of Combinatorial Theory, Series B, vol.37, issue.3, pp.254-269, 1984.
DOI : 10.1016/0095-8956(84)90058-3
URL : https://doi.org/10.1016/0095-8956(84)90058-3

D. Fron?ek, Locally linear graphs, Mathematica Slovaca, vol.39, issue.1, pp.3-6, 1989.

Z. Füredi and J. Pach, Traces of finite sets: extremal problems and geometric applications In: Extremal Problems for Finite Sets, pp.251-282, 1994.

M. L. Furst, J. L. Gross, and L. A. Mcgeoch, Finding a maximum-genus graph imbedding, Journal of the ACM, vol.35, issue.3, pp.523-534, 1988.
DOI : 10.1145/44483.44485

H. N. Gabow and M. Stallmann, An augmenting path algorithm for linear matroid parity, Combinatorica, vol.57, issue.2, pp.123-150, 1986.
DOI : 10.1137/1.9781611970265

T. Gallai, Kritische Graphen II, pp.373-395, 1963.

T. Gallai, Transitiv orientierbare Graphen, Acta Mathematica Academiae Scientiarum Hungaricae, vol.51, issue.1-2, pp.25-66, 1967.
DOI : 10.4153/CJM-1964-055-5

P. Gambette and S. Vialette, On Restrictions of Balanced 2-Interval Graphs, Lecture Notes in Computer Science, vol.4769, pp.55-65, 2007.
DOI : 10.1007/978-3-540-74839-7_6
URL : https://hal.archives-ouvertes.fr/hal-00141338

M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, pp.14-93, 1979.

M. R. Garey and D. S. Johnson, The Rectilinear Steiner Tree Problem is $NP$-Complete, SIAM Journal on Applied Mathematics, vol.32, issue.4, pp.826-834, 1977.
DOI : 10.1137/0132071

M. Gentner and D. Rautenbach, Feedback vertex sets in cubic multigraphs, Discrete Mathematics, vol.338, issue.12, pp.2179-2185, 2015.
DOI : 10.1016/j.disc.2015.05.029

P. A. Golovach, M. Johnson, D. Paulusma, and J. Song, A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs, Journal of Graph Theory, vol.15, issue.3-4, 2016.
DOI : 10.1016/0095-8956(80)90093-3

P. A. Golovach, D. Paulusma, and J. Song, Closing complexity gaps for coloring problems on H-free graphs, Information and Computation, vol.237, issue.100, pp.204-214, 2014.
DOI : 10.1016/j.ic.2014.02.004

F. Gurski, A comparison of two approaches for polynomial time algorithms computing basic graph parameters In: CoRR abs/0806, p.61, 2008.

A. Gyárfás, Problems from the world surrounding perfect graphs, In: Zastosowania Matematyki, vol.1934, issue.46, pp.413-441, 1987.

A. Gyárfás, Z. Li, R. Machado, A. Seb?-o, S. Thomassé et al., Complements of nearly perfect graphs, Journal of Combinatorics, vol.4, issue.3, pp.299-310, 2013.
DOI : 10.4310/JOC.2013.v4.n3.a2

A. Gyárfás, A. Seb?, and N. Trotignon, The chromatic gap and its extremes, Journal of Combinatorial Theory, Series B, vol.102, issue.5, pp.1155-1178, 2012.
DOI : 10.1016/j.jctb.2012.06.001

J. Harant, M. A. Henning, D. Rautenbach, and I. Schiermeyer, The independence number in graphs of maximum degree three, Discrete Mathematics, vol.308, issue.23, pp.5829-5833, 2008.
DOI : 10.1016/j.disc.2007.10.029

F. Harary and C. Holzmann, Line graphs of bipartite graphs, In: Revista de la Sociedad Matematica de Chile, vol.1, pp.19-22, 1974.

F. Harary, C. J. St, and . Nash-williams, On eulerian and hamiltonian graphs and line graphs, Bulletin canadien de math??matiques, vol.8, issue.0, pp.701-709, 1965.
DOI : 10.4153/CMB-1965-051-3

D. Haussler and E. Welzl, ??-nets and simplex range queries, Discrete & Computational Geometry, vol.11, issue.2, pp.127-151, 1987.
DOI : 10.1145/800061.808755

P. Haxell, A. Kostochka, and S. Thomassé, Packing and Covering Triangles in K 4-free Planar Graphs, Graphs and Combinatorics, vol.6, issue.5, pp.653-662, 2012.
DOI : 10.1007/BF01787705
URL : https://hal.archives-ouvertes.fr/lirmm-00806743

P. E. Haxell, Packing and covering triangles in graphs, Discrete Mathematics, vol.195, issue.1-3, pp.251-254, 1999.
DOI : 10.1016/S0012-365X(98)00183-6
URL : https://hal.archives-ouvertes.fr/lirmm-00806743

P. E. Haxell and A. D. Scott, On Lower Bounds for the Matching Number of Subcubic Graphs, Journal of Graph Theory, vol.64, issue.2, 2016.
DOI : 10.1007/s00373-007-0757-5

P. E. Haxell, A. V. Kostochka, and S. Thomassé, A stability theorem on fractional covering of triangles by edges, European Journal of Combinatorics, vol.33, issue.5, pp.799-806, 2012.
DOI : 10.1016/j.ejc.2011.09.024
URL : https://hal.archives-ouvertes.fr/lirmm-00806759

C. C. Heckman, On the tightness of the <mml:math altimg="si49.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mstyle displaystyle="false"><mml:mfrac><mml:mrow><mml:mn>5</mml:mn></mml:mrow><mml:mrow><mml:mn>14</mml:mn></mml:mrow></mml:mfrac></mml:mstyle></mml:math> independence ratio, Discrete Mathematics, vol.308, issue.15, pp.3169-3179, 2008.
DOI : 10.1016/j.disc.2007.06.044

C. C. Heckman and R. Thomas, Independent sets in triangle-free cubic planar graphs, Journal of Combinatorial Theory, Series B, vol.96, issue.2, pp.253-275, 2006.
DOI : 10.1016/j.jctb.2005.07.009
URL : https://doi.org/10.1016/j.jctb.2005.07.009

J. R. Henderson, Permutation decomposition of (0, 1)-matrices and decomposition transversals, 1971.

M. A. Henning, C. Löwenstein, and D. Rautenbach, Independent sets and matchings in subcubic graphs, Discrete Mathematics, vol.312, issue.11, pp.1900-1910, 2012.
DOI : 10.1016/j.disc.2012.03.002
URL : https://doi.org/10.1016/j.disc.2012.03.002

C. T. Hoàng, On the structure of (banner, odd hole)-free graphs In: CoRR abs/1510, p.2324, 2015.

Y. Huang and Y. Liu, Maximum genus and maximum nonseparating independent set of a 3-regular graph, Discrete Mathematics, vol.176, issue.1-3, pp.1-3, 1997.
DOI : 10.1016/S0012-365X(96)00299-3

S. Iwata, A weighted linear matroid parity algorithm, Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing , STOC 2017, pp.251-259
DOI : 10.1137/130949877

B. Jackson and K. Yoshimoto, Spanning even subgraphs of 3-edge-connected graphs, Journal of Graph Theory, vol.89, issue.1, pp.37-47, 2009.
DOI : 10.1002/jgt.20386

F. Joos, Independence and matching number in graphs with maximum degree 4, Discrete Mathematics, vol.323, issue.46, pp.1-6, 2014.
DOI : 10.1016/j.disc.2014.01.006

M. Kami´nskikami´nski, max-cut??and containment relations in graphs, Theoretical Computer Science, vol.438, pp.89-95, 2012.
DOI : 10.1016/j.tcs.2012.02.036

M. Kami´nskikami´nski, V. V. Lozin, and M. Milani?, Recent developments on graphs of bounded clique-width, Discrete Applied Mathematics, vol.157, issue.12, pp.2747-2761, 2009.
DOI : 10.1016/j.dam.2008.08.022

L. Kang, D. Wang, and E. Shan, Independent sets in <mml:math altimg="si15.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:mo>{</mml:mo><mml:mstyle mathvariant="normal"><mml:mi>claw</mml:mi></mml:mstyle><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:math>-free 4-regular graphs, Discrete Mathematics, vol.332, pp.40-44, 2014.
DOI : 10.1016/j.disc.2014.05.019

L. Kang, D. Wang, and E. Shan, THE INDEPENDENCE NUMBER OF CONNECTED (claw, $K_{4}$)-FREE 4-REGULAR GRAPHS, Taiwanese Journal of Mathematics, vol.17, issue.1, pp.275-285, 2013.
DOI : 10.11650/tjm.17.2013.2895

L. M. Kirousis, M. J. Serna, and P. G. Spirakis, Parallel Complexity of the Connected Subgraph Problem, SIAM Journal on Computing, vol.22, issue.3, pp.573-586, 1993.
DOI : 10.1137/0222039

T. Kloks, C. M. Lee, J. Liu-van-leeuwen, and L. Ku?era, New Algorithms for k-Face Cover, k-Feedback Vertex Set, and k-Disjoint Cycles on Plane and Planar Graphs, Lecture Notes in Computer Science, vol.2573, issue.48, pp.282-295, 2002.
DOI : 10.1007/3-540-36379-3_25

D. V. Korobitsin, On the complexity of domination number determination in monogenic classes of graphs, Discrete Mathematics and Applications, vol.2, issue.2, pp.191-200, 1992.
DOI : 10.1515/dma.1992.2.2.191

N. Korpelainen, Boundary Properties of Graphs, p.2012

N. Korpelainen, V. V. Lozin, D. S. Malyshev, and A. Tiskin, Boundary properties of graphs for algorithmic graph problems, Theoretical Computer Science, vol.412, issue.29, pp.3545-3554, 2011.
DOI : 10.1016/j.tcs.2011.03.001

N. Korpelainen, V. V. Lozin, and C. Mayhill, Split Permutation Graphs, Graphs and Combinatorics, vol.92, issue.3, pp.633-646, 2014.
DOI : 10.1016/j.jctb.2004.08.001

B. Korte and J. Vygen, Combinatorial Optimization. 4th. Algorithms and Combinatorics, 2007.

M. Kotrb?ík, A note on disjoint cycles, Information Processing Letters, vol.112, issue.4, pp.135-137, 2012.
DOI : 10.1016/j.ipl.2011.11.006

D. Král-', J. Kratochvíl, Z. Tuza, and G. J. Woeginger, Complexity of Coloring Graphs without Forbidden Induced Subgraphs, Lecture Notes in Computer Science, vol.2204, issue.100, pp.254-262, 2001.
DOI : 10.1007/3-540-45477-2_23

E. Kranakis, D. Krizanc, B. Ruf, J. Urrutia, and G. J. Woeginger, The VC-dimension of set systems defined by graphs, Discrete Applied Mathematics, vol.77, issue.3, pp.237-257, 1997.
DOI : 10.1016/S0166-218X(96)00137-0

J. Krausz, Démonstration nouvelle d'un théorème de Whitney sur les réseaux, In: Mat. Fiz. Lapok, vol.50, pp.75-85, 1943.

M. Krivelevich, On a conjecture of Tuza about packing and covering of triangles, Discrete Mathematics, vol.142, issue.1-3, pp.281-286, 1995.
DOI : 10.1016/0012-365X(93)00228-W

A. Labarre, Comment on Complexity of finding 2 vertex-disjoint (|V |/2)-cycles in cubic graphs? URL: http : / / cstheory . stackexchange . com / questions / 6107 / complexity -of -finding -2 -vertex -disjoint -v -2 -cycles -in -cubic -graphs (cit, p.32, 2011.

T. H. Lai and S. S. Wei, The edge Hamiltonian path problem is NP-complete for bipartite graphs, Information Processing Letters, vol.46, issue.1, pp.21-26, 1993.
DOI : 10.1016/0020-0190(93)90191-B

S. A. Lakshmanan, C. Bujtás, and Z. Tuza, Generalized line graphs: Cartesian products and complexity of recognition, In: Electr. J. Comb, vol.22, issue.40, pp.3-33, 2015.

S. A. Lakshmanan, C. Bujtás, and Z. Tuza, Induced cycles in triangle graphs, Discrete Applied Mathematics, vol.209, pp.264-275, 2016.
DOI : 10.1016/j.dam.2015.12.012

S. A. Lakshmanan, C. Bujtás, and Z. Tuza, Small Edge Sets Meeting all Triangles of a Graph, Graphs and Combinatorics, vol.26, issue.3, pp.381-392, 2012.
DOI : 10.1112/blms/26.4.321

R. Laskar and J. Pfaff, Domination and irredundance in split graphs, Mathematical Sciences, Clemson Univ, 1983.

V. B. Le, Gallai graphs and anti-Gallai graphs, Discrete Mathematics, vol.159, issue.1-3, pp.1-3, 1996.
DOI : 10.1016/0012-365X(95)00109-A
URL : https://doi.org/10.1016/0012-365x(95)00109-a

V. B. Le and E. Prisner, Iterated k-Line Graphs, In: Graphs and Combinatorics, vol.10, issue.2, pp.193-203, 1994.

P. G. Lehot, An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph, Journal of the ACM, vol.21, issue.4, pp.569-575, 1974.
DOI : 10.1145/321850.321853

J. Liu and C. Zhao, A new bound on the feedback vertex sets in cubic graphs, Discrete Mathematics, vol.148, issue.1-3, pp.119-131, 1996.
DOI : 10.1016/0012-365X(94)00268-N

S. C. Locke and F. Lou, Finding Independent Sets inK4-Free 4-Regular Connected Graphs, Journal of Combinatorial Theory, Series B, vol.71, issue.1, pp.85-110, 1997.
DOI : 10.1006/jctb.1997.1772
URL : https://doi.org/10.1006/jctb.1997.1772

D. Lokshtanov, M. Pilipczuk, and E. J. Van-leeuwen, Independence and Efficient Domination on P 6 -free Graphs, Proceedings of the Twenty-Seventh Annual ACM- SIAM Symposium on Discrete Algorithms. SODA '16. 2016, pp.1784-1803
DOI : 10.1137/1.9781611974331.ch124
URL : http://arxiv.org/pdf/1507.02163

L. Lovász, Matroid matching and some applications, Journal of Combinatorial Theory, Series B, vol.28, issue.2, pp.208-236, 1980.
DOI : 10.1016/0095-8956(80)90066-0

L. Lovász and M. D. Plummer, Matching Theory, pp.96-118, 1986.
DOI : 10.1090/chel/367

V. V. Lozin and D. Rautenbach, The tree-and clique-width of bipartite graphs in special classes, In: The Australasian Journal of Combinatorics, vol.34, pp.57-67, 2006.

J. Ma, X. Yu, and W. Zang, Approximate min-max relations on plane graphs, Journal of Combinatorial Optimization, vol.16, issue.1, pp.127-134, 2013.
DOI : 10.1007/BF01271272
URL : http://doi.org/10.1007/s10878-011-9440-0

D. S. Malyshev, A complexity dichotomy and a new boundary class for the dominating set problem, Journal of Combinatorial Optimization, vol.27, issue.3, pp.226-243, 2016.
DOI : 10.1137/0138030

D. S. Malyshev, Classes of graphs critical for the edge list-ranking problem, Journal of Applied and Industrial Mathematics, vol.8, issue.2, pp.245-255, 2014.
DOI : 10.1134/S1990478914020112

D. S. Malyshev, Continued sets of boundary classes of graphs for colorability problems, Russian), pp.41-51, 2009.

D. S. Malyshev and P. M. Pardalos, Critical hereditary graph classes: a survey, Optimization Letters, vol.21, issue.8, pp.1-20, 2015.
DOI : 10.1287/moor.18.1.1

G. J. Minty, On maximal independent sets of vertices in claw-free graphs, Journal of Combinatorial Theory, Series B, vol.28, issue.3, pp.284-304, 1980.
DOI : 10.1016/0095-8956(80)90074-X

B. Mohar and C. Thomassen, Graphs on Surfaces, p.11, 2001.

H. Müller, Hamiltonian circuits in chordal bipartite graphs, Discrete Mathematics, vol.156, issue.1-3, pp.291-298, 1996.
DOI : 10.1016/0012-365X(95)00057-4

A. Munaro, Boundary classes for graph problems involving non-local properties, Theoretical Computer Science, vol.692
DOI : 10.1016/j.tcs.2017.06.012

A. Munaro, Bounded clique cover of some sparse graphs, Discrete Mathematics, vol.340, issue.9
DOI : 10.1016/j.disc.2017.04.004
URL : https://hal.archives-ouvertes.fr/hal-01568247

A. Munaro, On line graphs of subcubic triangle-free graphs, Discrete Mathematics, vol.340, issue.6
DOI : 10.1016/j.disc.2017.01.006
URL : https://hal.archives-ouvertes.fr/hal-01568249

A. Munaro, The VC-dimension of graphs with respect to <mml:math altimg="si14.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mi>k</mml:mi></mml:math>-connected subgraphs, Discrete Applied Mathematics, vol.211, pp.163-174, 2016.
DOI : 10.1016/j.dam.2016.04.016

L. Nebeský, A new characterization of the maximum genus of a graph, In: Czechoslovak Mathematical Journal, vol.31, issue.4, pp.604-613, 1981.

L. Nebeský, Characterizing the maximum genus of a connected graph, In: Czechoslovak Mathematical Journal, vol.43, issue.1, pp.177-185, 1993.

E. A. Nordhaus, B. M. Stewart, and A. T. White, On the maximum genus of a graph, Journal of Combinatorial Theory, Series B, vol.11, issue.3, pp.258-267, 1971.
DOI : 10.1016/0095-8956(71)90036-0

S. O. and D. B. West, Balloons, Cut-Edges, Matchings, and Total Domination in Regular Graphs of Odd Degree, In: Journal of Graph Theory, vol.64, issue.2, pp.116-131, 2010.

S. Olariu, Paw-free graphs, Information Processing Letters, vol.28, issue.1, pp.53-54, 1988.
DOI : 10.1016/0020-0190(88)90143-3

J. B. Orlin and G. Rinaldi, A Fast, Simpler Algorithm for the Matroid Parity Problem, 13th International Conference, pp.240-258, 2008.
DOI : 10.1007/978-3-540-68891-4_17

S. Oum and P. Seymour, Approximating clique-width and branch-width, Journal of Combinatorial Theory, Series B, vol.96, issue.4, pp.514-528, 2006.
DOI : 10.1016/j.jctb.2005.10.006
URL : https://doi.org/10.1016/j.jctb.2005.10.006

J. Oxley and G. Whittle, A Characterization of Tutte Invariants of 2-Polymatroids, Journal of Combinatorial Theory, Series B, vol.59, issue.2, pp.210-244, 1993.
DOI : 10.1006/jctb.1993.1067

G. Pap, Weighted linear matroid matching, Proceedings of the 8th Japanese- Hungarian Symposium on Discrete Mathematics and Its Applications. 2013, pp.411-413

C. H. Papadimitriou and M. Yannakakis, On Limited Nondeterminism and the Complexity of the V-C Dimension, Journal of Computer and System Sciences, vol.53, issue.2, pp.161-170, 1996.
DOI : 10.1006/jcss.1996.0058

D. Peterson, Gridline graphs: a review in two dimensions and an extension to higher dimensions, Discrete Applied Mathematics, vol.126, issue.2-3, pp.2-3, 2003.
DOI : 10.1016/S0166-218X(02)00200-7

J. Pfaff, R. Laskar, and S. T. Hedetniemi, NP-completeness of total and connected domination , and irredundance for bipartite graphs, Mathematical Sciences, Clemson Univ, 1983.

M. D. Plummer, Claw-free maximal planar graphs, In: Congressus Numerantium, vol.72, pp.9-23, 1990.

G. J. Puleo, Tuza???s Conjecture for graphs with maximum average degree less than <mml:math altimg="si22.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mn>7</mml:mn></mml:math>, European Journal of Combinatorics, vol.49, issue.64, pp.134-152, 2015.
DOI : 10.1016/j.ejc.2015.03.006

S. P. Radziszowski, Small Ramsey Numbers, In: Electronic Journal of Combinatorics, vol.1, 2014.

B. Randerath and I. Schiermeyer, Vertex Colouring and Forbidden Subgraphs ? A Survey, Graphs and Combinatorics, vol.20, issue.1, pp.1-40, 2004.
DOI : 10.1007/s00373-003-0540-1
URL : http://e-archive.informatik.uni-koeln.de/453/2/zaik2003-453.pdf

N. Robertson and P. D. Seymour, Graph minors. II. Algorithmic aspects of tree-width, Journal of Algorithms, vol.7, issue.3, pp.309-322, 1986.
DOI : 10.1016/0196-6774(86)90023-4
URL : https://doi.org/10.1006/jctb.1996.0059

N. Robertson and P. D. Seymour, Graph minors. V. Excluding a planar graph, Journal of Combinatorial Theory, Series B, vol.41, issue.1, pp.92-114, 1986.
DOI : 10.1016/0095-8956(86)90030-4
URL : https://doi.org/10.1006/jctb.1996.0059

N. Robertson, D. Sanders, P. Seymour, and R. Thomas, The Four-Colour Theorem, Journal of Combinatorial Theory, Series B, vol.70, issue.1, pp.2-44, 1997.
DOI : 10.1006/jctb.1997.1750
URL : https://doi.org/10.1006/jctb.1997.1750

N. D. Roussopoulos, A max {m,n} algorithm for determining the graph H from its line graph G, Information Processing Letters, vol.2, issue.4, pp.108-112, 1973.
DOI : 10.1016/0020-0190(73)90029-X

N. Sauer, On the density of families of sets, Journal of Combinatorial Theory, Series A, vol.13, issue.1, pp.145-147, 1972.
DOI : 10.1016/0097-3165(72)90019-2

N. Sbihi, Algorithme de recherche d'un stable de cardinalite maximum dans un graphe sans etoile, Discrete Mathematics, vol.29, issue.1, pp.53-76, 1980.
DOI : 10.1016/0012-365X(90)90287-R
URL : https://doi.org/10.1016/0012-365x(90)90287-r

M. Schaefer, Deciding the Vapnik?????ervonenkis Dimension is???p3-complete, Journal of Computer and System Sciences, vol.58, issue.1, pp.177-182, 1999.
DOI : 10.1006/jcss.1998.1602
URL : https://doi.org/10.1006/jcss.1998.1602

M. Schaefer, Deciding the VC-dimension is ? p 3 -complete, II, 2000.
DOI : 10.1109/ccc.2000.856750

M. Schaefer and C. Umans, Completeness in the Polynomial-Time Hierarchy -A Compendium, In: SIGACT News, vol.33, issue.3, 2002.

A. Scott and P. Seymour, Induced subgraphs of graphs with large chromatic number. I. Odd holes, Journal of Combinatorial Theory, Series B, vol.121, 2015.
DOI : 10.1016/j.jctb.2015.10.002

S. Shelah, A combinatorial problem; stability and order for models and theories in infinitary languages, Pacific Journal of Mathematics, vol.41, issue.1, pp.247-261, 1972.
DOI : 10.2140/pjm.1972.41.247

E. Speckenmeyer, On feedback vertex sets and nonseparating independent sets in cubic graphs, Journal of Graph Theory, vol.49, issue.3, pp.405-412, 1988.
DOI : 10.1002/jgt.3190120311

E. Speckenmeyer, Untersuchungen zum Feedback Vertex Set Problem in ungerichteten Graphen, pp.31-117, 1983.

W. Staton, Some Ramsey-type numbers and the independence ratio, Transactions of the American Mathematical Society, vol.256, issue.57, pp.353-370, 1979.
DOI : 10.1090/S0002-9947-1979-0546922-6
URL : http://www.ams.org/tran/1979-256-00/S0002-9947-1979-0546922-6/S0002-9947-1979-0546922-6.pdf

M. Stehlík, Critical graphs with connected complements, Journal of Combinatorial Theory, Series B, vol.89, issue.2, pp.189-194, 2003.
DOI : 10.1016/S0095-8956(03)00069-8

Z. Tuza, A conjecture on triangles of graphs, Graphs and Combinatorics, vol.24, issue.4, pp.373-380, 1990.
DOI : 10.1007/BF01787705

R. Uehara, NP-complete problems on a 3-connected cubic planar graph and their applications, p.61, 1996.

S. Ueno, Y. Kajitani, and S. Gotoh, On the nonseparating independent set problem and feedback set problem for graphs with no vertex degree exceeding three, Discrete Mathematics, vol.72, issue.1-3, pp.355-360, 1988.
DOI : 10.1016/0012-365X(88)90226-9

V. N. Vapnik and A. Y. Chervonenkis, On the uniform convergence of relative frequencies of events to their probabilities, Theory of Probability and Its Applications, pp.264-280, 1971.

D. B. West, Introduction to Graph Theory, pp.46-63, 2001.

H. Whitney, Congruent Graphs and the Connectivity of Graphs, American Journal of Mathematics, vol.54, issue.1, pp.150-168, 1932.
DOI : 10.2307/2371086

N. H. Xuong, How to determine the maximum genus of a graph, Journal of Combinatorial Theory, Series B, vol.26, issue.2, pp.217-225, 1979.
DOI : 10.1016/0095-8956(79)90058-3

N. H. Xuong, Upper-embeddable graphs and related topics, Journal of Combinatorial Theory, Series B, vol.26, issue.2, pp.226-232, 1979.
DOI : 10.1016/0095-8956(79)90059-5

?. Résumé and . Dans-cette-thèse, hypergraphes permettent d'obtenir des propriétés combinatoires et algorithmiques souhaitables La plupart des paramètres que nous prenons en compte sont des instances spéciales des packings et transversals des hypergraphes Dans la première partie, nous allons nous concentrer sur les line graphs des graphes subcubiques sans triangle et nous allons démontrer que pour tous ces graphes il y a un independent set de taille au moins 3 10 |V (G)| et cette borne est optimale Conséquence immédiate: nous obtenons une borne inférieure optimale pour la taille d'un couplage maximum dans les graphes subcubiques sans triangle. De plus, nous montrons plusieurs résultats algorithmiques liés au FEEDBACK VERTEX SET, HAMILTONIAN CYCLE et HAMILTONIAN PATH quand restreints aux line graphs des graphes subcubiques sans triangle. Puis nous examinons trois hypergraphes ayant la propriété d'Erd? os-Pósa et nous cherchons à déterminer les fonctions limites optimales. Tout d'abord, nous apportons une fonction ?-bounding pour la classe des graphes subcubiques et nous étudions CLIQUE COVER: en répondant à une question de Cerioli et al. [31], nous montrons qu'il admet un PTAS pour les graphes planaires, nous considérons plusieurs paramètres des hypergraphes et nous étudions si les restrictions aux sous-classes des nous nous intéressons à la Conjecture de Tuza et nous montrons que la constante 2 peut être améliorée pour certains graphes sans K 4 et avec arêtes contenues dans au maximum quatre triangles et pour les graphes sans certains odd-wheels

. Enfin, nous nous concentrons sur la Conjecture de Jones: nous la démontrons dans le cas des graphes sans griffes avec degré maximal 4 et nous faisons quelques observations dans le cas des graphes subcubiques. Nous étudions ensuite la VC-dimension de certains hypergraphes résultants des graphes

. En-particulier, ensemble des sommets d'un certain graphe qui est induit par la famille de ses sous-graphes k-connexes. En généralisant les résultats de Kranakis et al. [115], nous fournissons des bornes supérieures et inférieures optimales pour la VC-dimension et nous montrons que son calcul est NP-complet, pour chacun k ? 1. Enfin , nous démontrons que ce problème (dans le cas k = 1) et le problème étroitement lié CONNECTED DOMINATING SET sont soit solvables en temps polynomial ou NP-complet, quand restreints aux classes de graphes obtenues en interdisant un seul sous-graphe induit, nous nous attaquons aux meta-questions suivantes

V. Quand-est-ce-qu, C. Set, . Dominating, C. Set, . Vertex et al., Existe-t-il des frontières séparant des instances " faciles " et " difficiles " ? Afin de répondre à ces questions, dans le cas des classes héréditaires, Alekseev [5] a introduit la notion de boundary class pour un problème NP-difficile et a montré qu'un problème ? est NP-difficile pour une classe héréditaire X finiment défini si et seulement si X contient un boundary class pour ?, Nous continuons la recherche des boundary classes pour les problèmes suivants: HAMILTONIAN CYCLE THROUGH SPECIFIED EDGE, HAMILTONIAN PATH