List strong edge coloring of planar graphs

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} $\chiup_{s}'(G)$ of a graph $G$ is the minimum number of colors in a strong edge coloring of $G$. In an analogous way, we can define the list version of strong edge coloring and list version of strong chromatic index $\chiup_{\mathrm{slist}}'(G)$. In this paper, we prove that if $G$ is a graph with $\Delta(G) \leq 4$ and maximum average degree less than $3$, then $\chiup_{\mathrm{slist}}'(G) \leq 3\Delta(G) + 1$. In addition, we prove that if $G$ is a planar graph with maximum degree at least $4$ and girth at least $7$, then $\chiup_{\mathrm{slist}}'(G) \leq 3\Delta(G)$.