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arXiv · 2602.03862

Strong edge-coloring of sparse graphs with Ore-degree 7 or 8

Runze Wang
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Abstract

In a strong edge-coloring of a graph $G=(V,E)$, any two edges of distance at most $2$ get distinct colors. The strong chromatic index of $G$, denoted by $\chi_s'(G)$, is the minimum number of colors needed in a strong edge-coloring of $G$. The Ore-degree of $G$ is defined by $\max\{d(u)+d(v):uv\in E\}$. In this paper, we apply the discharging method and make use of Hall's marriage theorem to prove two results toward a conjecture by Chen et al. First, we prove that if $G$ is a graph with Ore-degree $7$ and maximum average degree less than $\frac{34}{11}$, then $\chi_s'(G)\le 13$. This result improves the previous best bound from $\frac{40}{13}$ to $\frac{34}{11}$. Second, we prove that if $G$ is a graph with Ore-degree $8$ and maximum average degree less than $\frac{113}{31}$, then $\chi_s'(G)\le 20$.

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Runze Wang. 2026-01-27. Strong edge-coloring of sparse graphs with Ore-degree 7 or 8. https://arxiv.org/abs/2602.03862

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