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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.14388 |
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| _version_ | 1866910023396884480 |
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| author | Du, Shaofei Yuan, Kai |
| author_facet | Du, Shaofei Yuan, Kai |
| contents | In light of Lovász's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, this paper considers a natural variant: what if vertex-transitivity is relaxed, yet a high degree of symmetry--specifically edge-transitivity--is retained? To investigate this, we focus on the class of semisymmetric graphs, which are regular, edge-transitive, but not vertex-transitive. In this paper, it will be shown that every connected semisymmetric graph of order $2pq$, where $p$ and $q$ are two distinct primes contains a Hamilton cycle and that every connected cubic semisymmetric graph of order less than 3000 contains a Hamilton cycle too. Based on these observations, the following question is posed: construct a connected semisymmetric graph which has no Hamilton cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14388 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamilton Cycles in Semisymmetric Graphs Du, Shaofei Yuan, Kai Combinatorics 05C25, 05C45 In light of Lovász's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, this paper considers a natural variant: what if vertex-transitivity is relaxed, yet a high degree of symmetry--specifically edge-transitivity--is retained? To investigate this, we focus on the class of semisymmetric graphs, which are regular, edge-transitive, but not vertex-transitive. In this paper, it will be shown that every connected semisymmetric graph of order $2pq$, where $p$ and $q$ are two distinct primes contains a Hamilton cycle and that every connected cubic semisymmetric graph of order less than 3000 contains a Hamilton cycle too. Based on these observations, the following question is posed: construct a connected semisymmetric graph which has no Hamilton cycle. |
| title | Hamilton Cycles in Semisymmetric Graphs |
| topic | Combinatorics 05C25, 05C45 |
| url | https://arxiv.org/abs/2602.14388 |