The strong chromatic index of (3,Δ)-bipartite graphs

A strong edge-coloring of a graph G=(V,E) is a partition of its edge set E into induced matchings. We study bipartite graphs with one part having maximum degree at most 3 and the other part having maximum degree Δ. We show that every such graph has a strong edge-coloring using at most 3Δ colors. Our result confirms a conjecture of Brualdi and Quinn Massey (1993) for this class of bipartite graphs.