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

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 $\Delta$. For every such graph, we prove that a strong $4\Delta$-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. Strong edge-coloring of $(3, \Delta)$-bipartite graphs. Discrete Mathematics, Elsevier, 2016, 339 (1), ⟨10.1016/j.disc.2015.08.026⟩. ⟨hal-01080279v2⟩

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