Hamilton cycles in regular graphs perturbed by a random 2-factor
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914003571179520 |
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| author | Cicely Henderson Longbrake, Sean Mao, Dingjia Morawski, Patryk |
| author_facet | Cicely Henderson Longbrake, Sean Mao, Dingjia Morawski, Patryk |
| contents | In this paper, we prove that for each $d \geq 2$, the union of a $d$-regular graph with a uniformly random $2$-factor on the same vertex set is Hamiltonian with high probability. This resolves a conjecture by Draganić and Keevash for all values of $d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_21756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamilton cycles in regular graphs perturbed by a random 2-factor Cicely Henderson Longbrake, Sean Mao, Dingjia Morawski, Patryk Combinatorics In this paper, we prove that for each $d \geq 2$, the union of a $d$-regular graph with a uniformly random $2$-factor on the same vertex set is Hamiltonian with high probability. This resolves a conjecture by Draganić and Keevash for all values of $d$. |
| title | Hamilton cycles in regular graphs perturbed by a random 2-factor |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.21756 |