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arXiv · 2507.11927

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

Yunfang Tang·Zhiwei Bi
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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.

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Yunfang Tang, Zhiwei Bi. 2025-07-16. Strong list-chromatic index of subcubic graphs is at most 10. https://arxiv.org/abs/2507.11927

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