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Université d'Orléans |  |
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Université d'Orléans | |
| HAL: hal-00694158, version 1 |
| arXiv: 1205.0730 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2012-05-03) | v2 (2012-10-29) |
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| Reed's conjecture on some special classes of graphs |
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| Jean-Luc Fouquet 1Jean-Marie Vanherpe 1 |
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| (2012-04-27) |
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| Reed conjectured that for any graph $G$, $\chi(G) \leq \lceil \frac{\omega(G)+\Delta(G)+1}{2}\rceil$, where $\chi(G)$, $\omega(G)$, and $\Delta(G)$ respectively denote the chromatic number, the clique number and the maximum degree of $G$. In this paper, we verify this conjecture for some special classes of graphs, in particular for subclasses of $P_5$-free graphs or $Chair$-free graphs. |
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| 1: | Laboratoire d'Informatique Fondamentale d'Orléans (LIFO) |
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Université d'Orléans : EA4022 – Ecole Nationale Supérieure d'Ingénieurs de Bourges |
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| Subject | : | Computer Science/Discrete Mathematics |
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| Vertex coloring – Chromatic number – Clique number – Maximum degree |
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| hal-00694158, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00694158 | |
| oai:hal.archives-ouvertes.fr:hal-00694158 | |
| From: Jean-Marie Vanherpe | |
| Submitted on: Thursday, 3 May 2012 16:07:57 | |
| Updated on: Thursday, 3 May 2012 17:12:54 | |
