Minimum degree conditions for Hamilton $l$-cycles in $ k $-uniform hypergraphs
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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_ | 1866913727128797184 |
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| author | Han, Jie Sun, Lin Wang, Guanghui |
| author_facet | Han, Jie Sun, Lin Wang, Guanghui |
| contents | We show that for $ η>0 $ and sufficiently large $ n $, every 5-graph on $ n $ vertices with $δ_{2}(H)\ge (91/216+η)\binom{n}{3}$ contains a Hamilton 2-cycle. This minimum 2-degree condition is asymptotically best possible. Moreover, we give some related results on Hamilton $ \ell $-cycles with $ d $-degree for $\ell\le d \le k-1$ and $1\le \ell < k/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimum degree conditions for Hamilton $l$-cycles in $ k $-uniform hypergraphs Han, Jie Sun, Lin Wang, Guanghui Combinatorics We show that for $ η>0 $ and sufficiently large $ n $, every 5-graph on $ n $ vertices with $δ_{2}(H)\ge (91/216+η)\binom{n}{3}$ contains a Hamilton 2-cycle. This minimum 2-degree condition is asymptotically best possible. Moreover, we give some related results on Hamilton $ \ell $-cycles with $ d $-degree for $\ell\le d \le k-1$ and $1\le \ell < k/2$. |
| title | Minimum degree conditions for Hamilton $l$-cycles in $ k $-uniform hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.05275 |