Strong edge-coloring of $(3,\mathrm{\Delta })$-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 $\mathrm{\Delta }$. For every such graph, we prove that a strong $4\mathrm{\Delta }$-edge-coloring can always be obtained. Together with a result of Steger and Yu, this result confirms a conjecture of Faudree, Gy'arf'as, Schelp and Tuza for this class of graphs.