The strong chromatic index of $(3,\Delta )$-bipartite graphs

Abstract

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 $\Delta$. We show that every such graph has a strong edge-coloring using at most $3\Delta$ colors. Our result confirms a conjecture of Brualdi and Quinn Massey ~\cite{[BQ]} for this class of bipartite graphs.