# Choosability of a weighted path and free-choosability of a cycle

Abstract : A graph $G$ with a list of colors $L(v)$ and weight $w(v)$ for each vertex $v$ is $(L,w)$-colorable if one can choose a subset of $w(v)$ colors from $L(v)$ for each vertex $v$, such that adjacent vertices receive disjoint color sets. In this paper, we give necessary and sufficient conditions for a weighted path to be $(L,w)$-colorable for some list assignments $L$. Furthermore, we solve the problem of the free-choosability of a cycle.
Keywords :
Type de document :
Pré-publication, Document de travail
9 pages. 2011
Domaine :

https://hal.archives-ouvertes.fr/hal-00484445
Contributeur : Yves Aubry <>
Soumis le : lundi 16 mai 2011 - 14:15:49
Dernière modification le : lundi 16 mai 2011 - 15:56:45
Document(s) archivé(s) le : mercredi 17 août 2011 - 02:37:53

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### Identifiants

• HAL Id : hal-00484445, version 3
• ARXIV : 1005.5602

### Citation

Yves Aubry, Jean-Christophe Godin, Olivier Togni. Choosability of a weighted path and free-choosability of a cycle. 9 pages. 2011. <hal-00484445v3>

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