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arXiv · 1412.2624

Strong edge-coloring of $(3, Δ)$-bipartite graphs

Julien Bensmail·Aurélie Lagoutte·Petru Valicov
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Abstract

A strong edge-coloring of a graph $G$ is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose one part is of maximum degree at most $3$ and the other part is of maximum degree $Δ$. For every such graph, we prove that a strong $4Δ$-edge-coloring can always be obtained. Together with a result of Steger and Yu, this result confirms a conjecture of Faudree, Gyárfás, Schelp and Tuza for this class of graphs.

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Julien Bensmail, Aurélie Lagoutte, Petru Valicov. 2015-08-18. Strong edge-coloring of $(3, Δ)$-bipartite graphs. https://arxiv.org/abs/1412.2624

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