Strong list-chromatic index of subcubic graphs is at most 10
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911059380535296 |
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| author | Tang, Yunfang Bi, Zhiwei |
| author_facet | Tang, Yunfang Bi, Zhiwei |
| contents | 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 $χ_{s}'(G)$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_11927 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong list-chromatic index of subcubic graphs is at most 10 Tang, Yunfang Bi, Zhiwei Combinatorics 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 $χ_{s}'(G)$, 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. |
| title | Strong list-chromatic index of subcubic graphs is at most 10 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.11927 |