The star edge coloring of cubic Halin graphs with star chromatic index $5$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917085417832448 |
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| author | Hu, Xingxing Tang, Yunfang |
| author_facet | Hu, Xingxing Tang, Yunfang |
| contents | The star chromatic index of a graph $G$, denoted by $χ'_{st}(G) $, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored. Casselgren et al. and Hou et al. independently proved that the star chromatic index of a cubic Halin graph, except a special graph, is at most $6$. It remains an open problem to determine which of such graphs have star chromatic index $5$. In this paper, we show that if $G\ne N_{e_2}$ is a cubic Halin graph whose tree is a caterpillar or a complete tree, then $χ'_{st}(G)=5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The star edge coloring of cubic Halin graphs with star chromatic index $5$ Hu, Xingxing Tang, Yunfang Combinatorics The star chromatic index of a graph $G$, denoted by $χ'_{st}(G) $, is the minimum number of colors needed to properly color the edges of $G$ such that no path or cycle of length four is bi-colored. Casselgren et al. and Hou et al. independently proved that the star chromatic index of a cubic Halin graph, except a special graph, is at most $6$. It remains an open problem to determine which of such graphs have star chromatic index $5$. In this paper, we show that if $G\ne N_{e_2}$ is a cubic Halin graph whose tree is a caterpillar or a complete tree, then $χ'_{st}(G)=5$. |
| title | The star edge coloring of cubic Halin graphs with star chromatic index $5$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.13140 |