Tight Hamiltonicity from dense links of triples
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918107417673728 |
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| author | Lang, Richard Schacht, Mathias Volec, Jan |
| author_facet | Lang, Richard Schacht, Mathias Volec, Jan |
| contents | We show that for all $k\geq 4$, $\varepsilon >0$, and $n$ sufficiently large, every $k$-uniform hypergraph on $n$ vertices in which each set of $k-3$ vertices is contained in at least $(5/8 + \varepsilon) \binom{n}{3}$ edges contains a tight Hamilton cycle. This is asymptotically best possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_14518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tight Hamiltonicity from dense links of triples Lang, Richard Schacht, Mathias Volec, Jan Combinatorics 05C35, 05C45, 05C65 We show that for all $k\geq 4$, $\varepsilon >0$, and $n$ sufficiently large, every $k$-uniform hypergraph on $n$ vertices in which each set of $k-3$ vertices is contained in at least $(5/8 + \varepsilon) \binom{n}{3}$ edges contains a tight Hamilton cycle. This is asymptotically best possible. |
| title | Tight Hamiltonicity from dense links of triples |
| topic | Combinatorics 05C35, 05C45, 05C65 |
| url | https://arxiv.org/abs/2403.14518 |