Hamiltonian Cycles in Subdivided Doubles
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915566411841536 |
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| author | Eppstein, David |
| author_facet | Eppstein, David |
| contents | The subdivided double construction on 4-regular graphs was used by Potočnik and Wilson to explore semi-symmetric (edge-transitive but not vertex-transitive) graphs, and can be used to construct every semi-symmetric 4-regular graph that contains a pair of twin vertices. We show that (regardless of symmetry) subdivided doubles have another curious property: they have exponentially many Hamiltonian cycles each of which is complementary to another Hamiltonian cycle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18359 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Cycles in Subdivided Doubles Eppstein, David Combinatorics 05C76, 05C45 The subdivided double construction on 4-regular graphs was used by Potočnik and Wilson to explore semi-symmetric (edge-transitive but not vertex-transitive) graphs, and can be used to construct every semi-symmetric 4-regular graph that contains a pair of twin vertices. We show that (regardless of symmetry) subdivided doubles have another curious property: they have exponentially many Hamiltonian cycles each of which is complementary to another Hamiltonian cycle. |
| title | Hamiltonian Cycles in Subdivided Doubles |
| topic | Combinatorics 05C76, 05C45 |
| url | https://arxiv.org/abs/2510.18359 |