| Type de publication : |
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Preprint, Working Paper, Document sans référence, etc. |
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| Domaine : |
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Informatique/Mathématique discrète
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| Titre : |
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On parcimonious edge-colouring of graphs with maximum degree three |
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| Auteur(s) : |
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Jean-Luc Fouquet 1, Jean-Marie Vanherpe 1 |
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| Laboratoire : |
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| Résumé : |
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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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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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2006 |
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| Mots Clés : |
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Cubic graphs – edge partition |
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