Strong edge-coloring of sparse graphs with Ore-degree 7 or 8
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910010914635776 |
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| author | Wang, Runze |
| author_facet | Wang, Runze |
| contents | 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 $χ_s'(G)$, 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 $χ_s'(G)\le 13$. 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 $χ_s'(G)\le 20$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03862 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong edge-coloring of sparse graphs with Ore-degree 7 or 8 Wang, Runze Combinatorics 05C15 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 $χ_s'(G)$, 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 $χ_s'(G)\le 13$. 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 $χ_s'(G)\le 20$. |
| title | Strong edge-coloring of sparse graphs with Ore-degree 7 or 8 |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2602.03862 |