An exact Ore-degree condition for Hamilton cycles in oriented graphs
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866915373324959744 |
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| author | Chang, Yulin Cheng, Yangyang Dai, Tianjiao Ouyang, Qiancheng Wang, Guanghui |
| author_facet | Chang, Yulin Cheng, Yangyang Dai, Tianjiao Ouyang, Qiancheng Wang, Guanghui |
| contents | An oriented graph is a digraph that contains no 2-cycles, i.e., there is at most one arc between any two vertices. We show that every oriented graph $G$ of sufficiently large order $n$ with $\mathrm{deg}^+(x) +\mathrm{deg}^{-}(y)\geq (3n-3)/4$ whenever $G$ does not have an edge from $x$ to $y$ contains a Hamilton cycle. This is best possible and solves a problem of Kühn and Osthus from 2012. Our result generalizes the result of Keevash, Kühn, and Osthus and improves the asymptotic bound obtained by Kelly, Kühn, and Osthus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exact Ore-degree condition for Hamilton cycles in oriented graphs Chang, Yulin Cheng, Yangyang Dai, Tianjiao Ouyang, Qiancheng Wang, Guanghui Combinatorics An oriented graph is a digraph that contains no 2-cycles, i.e., there is at most one arc between any two vertices. We show that every oriented graph $G$ of sufficiently large order $n$ with $\mathrm{deg}^+(x) +\mathrm{deg}^{-}(y)\geq (3n-3)/4$ whenever $G$ does not have an edge from $x$ to $y$ contains a Hamilton cycle. This is best possible and solves a problem of Kühn and Osthus from 2012. Our result generalizes the result of Keevash, Kühn, and Osthus and improves the asymptotic bound obtained by Kelly, Kühn, and Osthus. |
| title | An exact Ore-degree condition for Hamilton cycles in oriented graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.04273 |