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| HAL: hal-00484445, version 3 |
| arXiv: 1005.5602 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-05-31) | v2 (2011-03-20) | v3 (2011-05-16) |
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| Choosability of a weighted path and free-choosability of a cycle |
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| Yves Aubry 1Jean-Christophe Godin 2 |
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| (2011-05-13) |
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| 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. |
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| 1: | Institut de Mathématiques de Luminy (IML) |
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CNRS : UPR9016 |
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| 2: | Institut de mathématiques de Luminy (IML) |
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CNRS : UMR6206 – Université de la Méditerranée - Aix-Marseille II |
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| 3: | Laboratoire Electronique, Informatique et Image (Le2i) |
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Université de Bourgogne – Arts et Métiers ParisTech – CNRS : UMR6306 |
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| Subject | : | Mathematics/Combinatorics Computer Science/Discrete Mathematics |
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| Coloring – Choosability – Free-choosability – Cycles. |
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| Attached file list to this document: | ||||||||||
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| hal-00484445, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00484445 | |
| oai:hal.archives-ouvertes.fr:hal-00484445 | |
| From: Yves Aubry | |
| Submitted on: Monday, 16 May 2011 14:15:49 | |
| Updated on: Monday, 16 May 2011 15:56:45 | |
