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arXiv · 1403.2339

Free choosability of the cycle

Yves Aubry·Jean-Christophe Godin·Olivier Togni
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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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Yves Aubry, Jean-Christophe Godin, Olivier Togni. 2014-03-10. Free choosability of the cycle. https://arxiv.org/abs/1403.2339

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