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

TL;DR

This paper proves that all subcubic graphs have a strong list-chromatic index at most 10, improving previous bounds and extending results from strong edge-coloring to list-coloring.

Contribution

It establishes a new upper bound of 10 for the strong list-chromatic index of subcubic graphs, strengthening prior results on strong edge-coloring.

Findings

Subcubic graphs have a strong list-chromatic index at most 10.

The result improves previous bounds on strong edge-coloring.

Extends the strong edge-coloring results to list-coloring for graphs with edge weight at most 6.

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 $\chi_{s}'(G)$, 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 $\max\limits_{uv\in E(G)}\{(d_G(u)+d_G(v))\}$. 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.