# 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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Type de document :
Article dans une revue
Graphs and Combinatorics, Springer Verlag, 2016, May 2016, Volume 32 (Issue 3, pp. 851-859), pp.DOI 10.1007/s00373-015-1625-3
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https://hal.archives-ouvertes.fr/hal-00957298
Contributeur : Yves Aubry <>
Soumis le : lundi 10 mars 2014 - 09:56:35
Dernière modification le : samedi 30 avril 2016 - 09:47:35
Document(s) archivé(s) le : mardi 10 juin 2014 - 11:00:15

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### Identifiants

• HAL Id : hal-00957298, version 1
• ARXIV : 1403.2339

### Citation

Yves Aubry, Jean-Christophe Godin, Olivier Togni. Free choosability of the cycle. Graphs and Combinatorics, Springer Verlag, 2016, May 2016, Volume 32 (Issue 3, pp. 851-859), pp.DOI 10.1007/s00373-015-1625-3. <hal-00957298>

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