Free choosability of the cycle

Abstract : A graph $G$ is free $(a,b)$-choosable if for any vertex $v$ with $b$ colors assigned and for any list of colors of size $a$ associated with each vertex $u\ne v$, the coloring can be completed by choosing for $u$ a subset of $b$ colors such that adjacent vertices are colored with disjoint color sets. In this note, a necessary and sufficient condition for a cycle to be free $(a,b)$-choosable is given. As a corollary, some choosability results are derived for graphs in which cycles are connected by a tree structure.
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Graphs and Combinatorics, Springer Verlag, 2016, 32 (3), pp.851-859. 〈10.1007/s00373-015-1625-3〉
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Soumis le : lundi 10 mars 2014 - 09:56:35
Dernière modification le : mercredi 12 septembre 2018 - 01:26:21
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Yves Aubry, Jean-Christophe Godin, Olivier Togni. Free choosability of the cycle. Graphs and Combinatorics, Springer Verlag, 2016, 32 (3), pp.851-859. 〈10.1007/s00373-015-1625-3〉. 〈hal-00957298〉



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