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Université d'Orléans |  |
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Université d'Orléans | |
| HAL: hal-00325253, version 2 |
| arXiv: 0809.4747 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2008-09-27) | v2 (2009-04-08) | v3 (2009-04-25) | v4 (2010-07-15) | v5 (2011-09-28) | v6 (2012-01-28) |
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| On parcimonious edge-colouring of graphs with maximum degree three |
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| Jean-Luc Fouquet 1Jean-Marie Vanherpe 1 |
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| (2006) |
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| In a graph $G$ of maximum degree $\Delta$ let $\gamma$ denote the largest fraction of edges that can be $\Delta$ edge-coloured. Albertson and Haas showned that $\gamma \geq \frac{13}{15}$ when $G$ is cubic \cite{AlbHaa}. We show here that this result can be extended to graphs with maximum degree $3$ with the exception of a graph on $5$ vertices. Moreover, there are exactly two graphs with maximum degree $3$ (one being obviously Petersen's graph) for which $\gamma = \frac{13}{15}$. This extends a result given in \cite{Ste04}. These results are obtained in giving structural properties of the so called $\delta-$minimum edge colourings for graphs with maximum degree $3$ |
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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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| Cubic graphs – edge partition |
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| hal-00325253, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00325253 | |
| oai:hal.archives-ouvertes.fr:hal-00325253 | |
| From: Jean-Marie Vanherpe | |
| Submitted on: Wednesday, 8 April 2009 10:47:11 | |
| Updated on: Wednesday, 8 April 2009 10:50:01 | |
