An excluded minor theorem for the 6-wheel
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866909044111835136 |
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| author | Chen, Zijun Xu, Yuqi Yang, Weihua |
| author_facet | Chen, Zijun Xu, Yuqi Yang, Weihua |
| contents | For each integer $n \geq 3$, the wheel graph $W_n$ is defined as the graph obtained by connecting a single vertex to all vertices of a cycle of length $n$. In particular, $W_6$ can be uniquely obtained from the Petersen graph by contracting three edges incident to a common vertex. Gubser provided a characterization of all 3-connected planar $W_6$-minor-free graphs. In this paper, we complete the characterization of $W_6$-minor-free graphs by determining the 3-connected nonplanar cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15125 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An excluded minor theorem for the 6-wheel Chen, Zijun Xu, Yuqi Yang, Weihua Combinatorics 05C83 For each integer $n \geq 3$, the wheel graph $W_n$ is defined as the graph obtained by connecting a single vertex to all vertices of a cycle of length $n$. In particular, $W_6$ can be uniquely obtained from the Petersen graph by contracting three edges incident to a common vertex. Gubser provided a characterization of all 3-connected planar $W_6$-minor-free graphs. In this paper, we complete the characterization of $W_6$-minor-free graphs by determining the 3-connected nonplanar cases. |
| title | An excluded minor theorem for the 6-wheel |
| topic | Combinatorics 05C83 |
| url | https://arxiv.org/abs/2605.15125 |