. Lemma-5, If GK(d, n) is Hamiltonian and n is odd, then there is a complete Berge

]. J. References, G. Bang-jensen, and . Gutin, Digraphs: theory, algorithms and applications, 2010.

J. Bondy and U. Murty, Graph Theory with applications, 2008.
DOI : 10.1007/978-1-349-03521-2

Z. Lonc and P. Naroski, On tours that contain all edges of a hypergraph, The electronic journal of combinatorics, p.17, 2010.

J. Bermond, Hamiltonian Decompositions of Graphs, Directed Graphs and Hypergraphs, Ann. Discrete Math, vol.3, pp.21-28, 1977.
DOI : 10.1016/S0167-5060(08)70494-1

P. Keevash, D. Kühn, R. Mycroft, and D. Osthus, Loose Hamilton cycles in hypergraphs, Discrete Mathematics, vol.311, issue.7, pp.311-544, 2011.
DOI : 10.1016/j.disc.2010.11.013

D. Kühn, R. Mycroft, and D. Osthus, Hamilton ???-cycles in uniform hypergraphs, Journal of Combinatorial Theory, Series A, vol.117, issue.7, pp.910-927, 2010.
DOI : 10.1016/j.jcta.2010.02.010

E. Arkin, M. Held, J. S. Mitchell, and S. Skiena, Hamilton triangulations for fast rendering, Proceedings of the Second Annual European Symposium on Algorithms, ESA '94, pp.36-47, 1994.

J. Bartholdi, I. , and P. Goldsman, Multiresolution indexing of triangulated irregular networks, IEEE Transactions on Visualization and Computer Graphics, vol.10, issue.4, pp.484-495, 2004.
DOI : 10.1109/TVCG.2004.14

J. Bartholdi, I. , and P. Goldsman, The vertex-adjacency dual of a triangulated irregular network has a Hamiltonian cycle, Operations Research Letters, vol.32, issue.4, pp.304-308, 2004.
DOI : 10.1016/j.orl.2003.11.005

A. Dudek, A. Frieze, and A. Ruci´nskiruci´nski, Rainbow hamilton cycles in uniform hypergraphs, Electronic Journal of Combinatorics, vol.19, p.46, 2012.

J. Bermond, R. W. Dawes, and F. Ergincan, De Bruijn and Kautz bus networks, 3¡205::AID-NET5¿3.0.CO;2-P, pp.205-218, 1997.

J. Bermond and C. Peyrat, De Bruijn and Kautz networks: a competitor for the hypercube?, Proceedings of the 1st European Workshop on Hypercubes and Distributed Computers, pp.279-293, 1989.

M. Imase and M. Itoh, Design to Minimize Diameter on Building-Block Network, IEEE Transactions on Computers, vol.30, issue.6, pp.30-439, 1981.
DOI : 10.1109/TC.1981.1675809

S. Reddy, D. Pradhan, and J. , Directed graphs with minimal diameter and maximal connectivity, 1980.

D. Du, D. F. Hsu, and F. K. Hwang, The Hamiltonian property of consecutive-d digraphs, Mathematical and Computer Modelling, vol.17, issue.11, pp.61-63, 1993.
DOI : 10.1016/0895-7177(93)90253-U

J. Bermond and F. Ergincan, Bus interconnection networks, Bus interconnection networks, pp.1-15, 1996.
DOI : 10.1016/0166-218X(95)00046-T

J. Bermond, F. Ergincan, M. Syska, and Q. Festschrift, Line Directed Hypergraphs, Lecture Notes in Computer Science, vol.6805, pp.25-34, 2011.
DOI : 10.1007/978-3-642-28368-0_5
URL : https://hal.archives-ouvertes.fr/hal-00643785

D. Ferrero and C. Padró, Connectivity and fault-tolerance of hyperdigraphs, Discrete Applied Mathematics, vol.117, issue.1-3, pp.15-26, 2002.
DOI : 10.1016/S0166-218X(00)00333-4

D. Ferrero and C. Padró, Partial line directed hypergraphs, Networks, vol.32, issue.2, pp.61-67, 2002.
DOI : 10.1002/net.10013

V. Batagelj and T. Pisanski, On partially directed Eulerian multigraphs, Publ. de l'Inst, Math. Soc, vol.25, issue.39, pp.16-24, 1979.

J. Bang-jensen and S. Thomassé, Decompositions and orientations of hypergraphs, Tech. Rep, vol.10, p.IMADA, 2001.

G. Ducoffe, Eulerian and Hamiltonian directed hypergraphs, Research Report INRIA, vol.7893, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00674655

D. Du and D. Hsu, On Hamiltonian consecutive-d digraphs, Banach Center Publications, vol.25, pp.47-55, 1989.

D. Du, D. F. Hsu, F. K. Hwang, and X. M. Zhang, The Hamiltonian property of generalized de Bruijn digraphs, Journal of Combinatorial Theory, Series B, vol.52, issue.1, pp.1-8, 1991.
DOI : 10.1016/0095-8956(91)90084-W

F. K. Hwang, The Hamiltonian property of linear functions, Operations Research Letters, vol.6, issue.3, pp.125-127, 1987.
DOI : 10.1016/0167-6377(87)90024-1

G. Chang, F. Hwang, and L. Tong, The hamiltonian property of the consecutive-3 digraph, Mathematical and Computer Modelling, vol.25, issue.11, pp.83-88, 1997.
DOI : 10.1016/S0895-7177(97)00086-1

G. Chang, F. Hwang, and L. Tong, The consecutive-4 digraphs are Hamiltonian, J. Graph Theory, pp.31-32, 1999.

D. Du, D. Hsu, and D. J. Kleitman, Modification of consecutive-d digraphs., in: Interconnection Networks and Mapping and Scheduling Parallel Computations, Proceedings DIMACS workshop February, pp.75-85, 1994.

D. Du, D. Hsu, and G. Peck, Connectivity of consecutive-d digraphs, Discrete Appl. Math, issue.92, pp.37-38, 1992.

D. Du, D. Hsu, H. Ngo, and G. Peck, On connectivity of consecutived digraphs, Discrete Math, pp.371-38410, 2002.

F. Cao, D. Du, F. Hsu, L. Hwang, and W. Wu, Super line-connectivity of consecutive-d digraphs, Discrete Mathematics, vol.183, issue.1-3, pp.27-38, 1998.
DOI : 10.1016/S0012-365X(97)00079-4

D. Barth and M. Heydemann, A new digraphs composition, 1995.

D. Barth and M. Heydemann, A new digraphs composition with applications to de Bruijn and generalized de Bruijn digraphs, Discrete Applied Mathematics, vol.77, issue.2, pp.99-118, 1996.
DOI : 10.1016/S0166-218X(96)00130-8

D. Coudert, Algorithmique et optimisation de réseaux de communications optiques, 2001.

J. Gómez, C. Padró, and S. Pérennes, Large generalized cycles, Discrete Applied Mathematics, vol.89, issue.1-3, pp.107-123, 1998.
DOI : 10.1016/S0166-218X(98)00120-6