A new bound for parsimonious edge-colouring of graphs with maximum degree three.
Résumé
In a graph $G$ of maximum degree $3$, let $\gamma(G)$ denote the largest fraction of edges that can be $3$ edge-coloured. Rizzi \cite{Riz09} showed that $\gamma(G) \geq 1-\frac{2 \strut}{\strut 3 g_{odd}(G)}$ where $g_{odd}(G)$ is the odd girth of $G$, when $G$ is triangle-free. In \cite{FouVan10a} we extended that result to graph with maximum degree $3$. We show here that $\gamma(G) \geq 1-\frac{2 \strut}{\strut 3 g_{odd}(G)+2}$, which leads to $\gamma(G) \geq \frac{15}{17}$ when considering graphs with odd girth at least $5$, distinct from the Petersen graph.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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