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14553 Contractible subgraphs, Thomassen’s conjecture and the dominating cycle conjecture for snarks

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Broersma, H.J. and Fijavž, G. and Kaiser, T. and Kuzel, R. and Ryjácek, Z. and Vrána, P. (2008) Contractible subgraphs, Thomassen’s conjecture and the dominating cycle conjecture for snarks. Discrete Mathematics, 308 (24). pp. 6064-6077. ISSN 0012-365X *** ISI Impact 0,548 ***

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Official URL: http://dx.doi.org/10.1016/j.disc.2007.11.026

Abstract

We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is Hamiltonian), by Thomassen (every 4-connected line graph is Hamiltonian) and by Fleischner (every cyclically 4-edge-connected cubic graph has either a 3-edge-coloring or a dominating cycle), which are known to be equivalent, are equivalent to the statement that every snark (i.e. a cyclically 4-edge-connected cubic graph of girth at least five that is not 3-edge-colorable) has a dominating cycle.

We use a refinement of the contractibility technique which was introduced by Ryjá?ek and Schelp in 2003 as a common generalization and strengthening of the reduction techniques by Catlin and Veldman and of the closure concept introduced by Ryjá?ek in 1997.

Item Type:	Article
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
ID Code:	14553
Status:	Published
Deposited On:	15 December 2008
Refereed:	Yes
International:	Yes
ISI Impact Factor:	0,548
More Information:	statistics metis

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