Strong edge-coloring of graphs with maximum edge weight seven
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912792537202688 |
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| author | Wang, Runze |
| author_facet | Wang, Runze |
| contents | A strong edge-coloring of a graph $G$ is an edge-coloring such that any two edges of distance at most two receive distinct colors. The minimum number of colors we need in order to give $G$ a strong edge-coloring is called the strong chromatic index of $G$, denoted by $χ_s'(G)$. The maximum edge weight of $G$ is defined to be $\max\{d(u)+d(v):\ uv\in E(G)\}$. In this paper, using the discharging method, we prove that if $G$ is a graph with maximum edge weight $7$ and maximum average degree less than $\frac{40}{13}$, then $χ_s'(G)\le 13$. Also, we determine the largest possible maximum average degree of a graph with given maximum edge weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20345 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong edge-coloring of graphs with maximum edge weight seven Wang, Runze Combinatorics 05C15 A strong edge-coloring of a graph $G$ is an edge-coloring such that any two edges of distance at most two receive distinct colors. The minimum number of colors we need in order to give $G$ a strong edge-coloring is called the strong chromatic index of $G$, denoted by $χ_s'(G)$. The maximum edge weight of $G$ is defined to be $\max\{d(u)+d(v):\ uv\in E(G)\}$. In this paper, using the discharging method, we prove that if $G$ is a graph with maximum edge weight $7$ and maximum average degree less than $\frac{40}{13}$, then $χ_s'(G)\le 13$. Also, we determine the largest possible maximum average degree of a graph with given maximum edge weight. |
| title | Strong edge-coloring of graphs with maximum edge weight seven |
| topic | Combinatorics 05C15 |
| url | https://arxiv.org/abs/2505.20345 |