List strong edge coloring of some classes of graphs

Abstract

A {\em strong edge coloring} of a graph is a proper edge coloring in which every color class is an induced matching. The {\em strong chromatic index} of a graph is the minimum number of colors needed to obtain a strong edge coloring. In an analogous way, we can define the list version of strong edge coloring and list version of strong chromatic index. In this paper, we prove that if $G$ is a graph with maximum degree at most four and maximum average degree less than $3$, then the list strong chromatic index is at most $3\Delta + 1$, where $\Delta$ is the maximum degree of $G$. In addition, we prove that if $G$ is a planar graph with maximum degree at least $4$ and girth at least $7$, then the list strong chromatic index is at most $3\Delta$.