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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.08105 |
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| _version_ | 1866909424517382144 |
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| author | Lehner, Florian Maghsoudi, Farzad Miraftab, Babak |
| author_facet | Lehner, Florian Maghsoudi, Farzad Miraftab, Babak |
| contents | In 1982, Durnberger proved that every connected Cayley graph of a finite group with a commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend this result to the infinite case. Additionally, we generalize this result to a broader class of infinite graphs $X$, where the automorphism group of $X$ contains a transitive subgroup $G$ with a cyclic commutator subgroup of prime order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_08105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $\Z_{p}$ as Commutator Subgroups Lehner, Florian Maghsoudi, Farzad Miraftab, Babak Combinatorics 05C25, 05C45, 05C63, 20E06, 20F05 In 1982, Durnberger proved that every connected Cayley graph of a finite group with a commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend this result to the infinite case. Additionally, we generalize this result to a broader class of infinite graphs $X$, where the automorphism group of $X$ contains a transitive subgroup $G$ with a cyclic commutator subgroup of prime order. |
| title | Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $\Z_{p}$ as Commutator Subgroups |
| topic | Combinatorics 05C25, 05C45, 05C63, 20E06, 20F05 |
| url | https://arxiv.org/abs/2412.08105 |