Strong list-chromatic index of subcubic graphs is at most 10

Abstract

A strong edge coloring of a graph $G$ is an assignment of colors to the edges of $G$ such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph $G$, denoted by ${\chi }_s^{\prime }(G)$, is the minimum number of colors needed for a strong edge coloring of $G$. The edge weight of a graph $G$ is defined to be $\underset{uv\in E(G)}{\max }\{(d_G(u)+d_G(v))\}$. It was proved in Chen et al in 2020 that every graph with edge weight at most 6 has a strong edge-coloring using at most 10 colors. In this paper, we consider the list version of strong edge-coloring. We strengthen this result by showing that every graph with edge weight at most 6 has a strong list-chromatic index at most 10. Specially, every subcubic graph has a strong list-chromatic index at most 10, which improves a result of Dai et al. in 2018.

6 pages,4 figures