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

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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