Z ) has at least k + 1 vertices, then |N G k?2 (Z )| ? (k + 1)(k ? 3, pp.2-3 ,
Tight Bounds for Linkages in Planar Graphs, Automata, Languages and Programming -38th International Colloquium, ICALP 2011, pp.110-121, 2011. ,
DOI : 10.1016/0166-218X(93)E0177-Z
Cycles Through 23 Vertices in 3-Connected Cubic Planar Graphs, Graphs and Combinatorics, vol.15, issue.4, pp.373-376, 1999. ,
DOI : 10.1007/s003730050046
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
(meta) kernelization, Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science, pp.629-638, 2009. ,
DOI : 10.1109/focs.2009.46
URL : https://hal.archives-ouvertes.fr/lirmm-01483628
Kernelization Lower Bounds by Cross-Composition, SIAM Journal on Discrete Mathematics, vol.28, issue.1, pp.277-305, 2014. ,
DOI : 10.1137/120880240
URL : http://arxiv.org/pdf/1206.5941.pdf
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
Graph Structure and Monadic Second-Order Logic -A Language-Theoretic Approach, Encyclopedia of mathematics and its applications, 2012. ,
The Bidimensional Theory of Bounded-Genus Graphs, SIAM Journal on Discrete Mathematics, vol.20, issue.2, pp.357-371, 2006. ,
DOI : 10.1137/040616929
Graph theory, Graduate Texts in Mathematics, vol.173, 2010. ,
In abstrakten Graphen vorhandene vollst??ndige 4-Graphen und ihre Unterteilungen, Mathematische Nachrichten, vol.2, issue.1-2, pp.61-85, 1960. ,
DOI : 10.1016/S1385-7258(54)50043-0
Parameterized complexity, 1999. ,
DOI : 10.1007/978-1-4612-0515-9
Fixed-parameter tractability and completeness. III. Some structural aspects of the W hierarchy, Complexity theory, pp.191-225, 1993. ,
DOI : 10.1137/s0097539792228228
URL : http://homepages.ecs.vuw.ac.nz/~downey/publications/1.pdf
Fixed-parameter tractability and completeness, 21st Manitoba Conference on Numerical Mathematics and Computing, pp.161-178, 1991. ,
DOI : 10.1137/s0097539792228228
URL : http://homepages.ecs.vuw.ac.nz/~downey/publications/1.pdf
Fixed-Parameter Tractability and Completeness I: Basic Results, SIAM Journal on Computing, vol.24, issue.4, pp.873-921, 1995. ,
DOI : 10.1137/S0097539792228228
URL : http://homepages.ecs.vuw.ac.nz/~downey/publications/1.pdf
Fixed-parameter tractability and completeness II: On completeness for W[1], Theoretical Computer Science, vol.141, issue.1-2, pp.109-131, 1995. ,
DOI : 10.1016/0304-3975(94)00097-3
Fundamentals of Parameterized Complexity, Texts in Computer Science, 2013. ,
DOI : 10.1007/978-1-4471-5559-1
Remarks on a paper of Pósa, Magyar Tud. Akad. Mat. Kutató Int. Közl, vol.7, pp.227-229, 1962. ,
A generalization of Dirac's theorem on cycles through k vertices in k-connected graphs, Discrete Mathematics, vol.307, issue.7-8, pp.878-884, 2007. ,
DOI : 10.1016/j.disc.2005.11.052
Contraction obstructions for treewidth, Journal of Combinatorial Theory, Series B, vol.101, issue.5, pp.302-314, 2011. ,
DOI : 10.1016/j.jctb.2011.02.008
URL : https://doi.org/10.1016/j.jctb.2011.02.008
The Planar Hamiltonian Circuit Problem is NP-Complete, SIAM Journal on Computing, vol.5, issue.4, pp.704-714, 1976. ,
DOI : 10.1137/0205049
Embedding grids in surfaces, European Journal of Combinatorics, vol.25, issue.6, pp.785-792, 2004. ,
DOI : 10.1016/j.ejc.2003.07.007
Hypohamiltonian facets of the symmetric travelling salesman polytope, Zeitschrift für Angewandte Mathematik und Mechanik, pp.469-471, 1977. ,
Improved bounds on the planar branchwidth with respect to the largest grid minor size, Algorithms and Computation -21st International Symposium, pp.85-96, 2010. ,
A shorter proof of the graph minor algorithm, Proceedings of the 42nd ACM symposium on Theory of computing, STOC '10, 2010. ,
DOI : 10.1145/1806689.1806784
Invitation to fixed-parameter algorithms, 2002. ,
DOI : 10.1093/acprof:oso/9780198566076.001.0001
AN IMPROVED ALGORITHM FOR FINDING TREE DECOMPOSITIONS OF SMALL WIDTH, International Journal of Foundations of Computer Science, vol.11, issue.03, pp.365-371, 2000. ,
DOI : 10.1016/0095-8956(88)90052-4
A nine vertex theorem for 3-connected claw- free graphs, Studia Scientiarum Mathematicarum Hungarica, vol.38, issue.1-4, pp.233-244, 2001. ,
DOI : 10.1556/SScMath.38.2001.1-4.16
Graph Minors. XXII. Irrelevant vertices in linkage problems, Journal of Combinatorial Theory, Series B, vol.102, issue.2, pp.530-563, 2012. ,
DOI : 10.1016/j.jctb.2007.12.007
URL : https://doi.org/10.1006/jctb.1996.0059
Graph minors. X. Obstructions to tree-decomposition, Journal of Combinatorial Theory, Series B, vol.52, issue.2, pp.153-190, 1991. ,
DOI : 10.1016/0095-8956(91)90061-N
URL : https://doi.org/10.1006/jctb.1996.0059
Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995. ,
DOI : 10.1006/jctb.1995.1006
URL : https://doi.org/10.1006/jctb.1996.0059
Graph Minors .XIII. The Disjoint Paths Problem, Journal of Combinatorial Theory, Series B, vol.63, issue.1, pp.65-110, 1995. ,
DOI : 10.1006/jctb.1995.1006
URL : https://doi.org/10.1006/jctb.1996.0059
Graph minors. XXI. Graphs with unique linkages, Journal of Combinatorial Theory, Series B, vol.99, issue.3, pp.583-616, 2009. ,
DOI : 10.1016/j.jctb.2008.08.003
URL : https://doi.org/10.1006/jctb.1996.0059
Cycles and connectivity in graphs, Journal canadien de math??matiques, vol.19, issue.0, pp.1319-1328, 1967. ,
DOI : 10.4153/CJM-1967-121-2