Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908436360331264 |
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| author | Chen, Huye Li, Jingjian Yu, Hao |
| author_facet | Chen, Huye Li, Jingjian Yu, Hao |
| contents | After long-term efforts, the Hamilton path (cycle) problem for connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally resolved in 2021, see [10]. Fifteen years ago, mathematicians began addressing this problem for graphs of order $2pq$. Among these studies, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p \neq 7$ is a prime) contains a Hamilton path, with the exception of a family of graphs that was recently confirmed in [11]. In this paper, we achieve a further result: every connected vertex-transitive graph of order $10p$ (where $p$ is a prime) contains a Hamilton cycle, except for the truncation of the Petersen graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19888 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamilton Cycles In Vertex-Transitive Graphs of Order 10p Chen, Huye Li, Jingjian Yu, Hao Combinatorics After long-term efforts, the Hamilton path (cycle) problem for connected vertex-transitive graphs of order $pq$ (where $p$ and $q$ are primes) was finally resolved in 2021, see [10]. Fifteen years ago, mathematicians began addressing this problem for graphs of order $2pq$. Among these studies, it was proved in 2012 (see [21]) that every connected vertex-transitive graph of order $10p$ (where $p \neq 7$ is a prime) contains a Hamilton path, with the exception of a family of graphs that was recently confirmed in [11]. In this paper, we achieve a further result: every connected vertex-transitive graph of order $10p$ (where $p$ is a prime) contains a Hamilton cycle, except for the truncation of the Petersen graph. |
| title | Hamilton Cycles In Vertex-Transitive Graphs of Order 10p |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.19888 |