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arXiv · 2609.33945

Strong edge coloring of graphs with maximum degree $6$

Runze Wang
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Abstract

Let $G$ be a graph. Under a strong edge coloring of $G$, every color class is an induced matching. The strong chromatic index of $G$, denoted by $χ'_s(G)$, is the smallest integer $k$ such that $G$ admits a strong edge coloring with $k$ colors. Denote by $Δ(G)$ the maximum degree of $G$. In this paper, we prove that every graph $G$ with $Δ(G)\le 6$ satisfies $χ'_s(G)\le 57$, improving the best known upper bound $60$.

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Runze Wang. 2026-09-27. Strong edge coloring of graphs with maximum degree $6$. https://arxiv.org/abs/2609.33945

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