The threshold for loose Hamilton cycles in random hypergraph
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913723467169792 |
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| author | Frieze, Alan Perez-Gimenez, Xavier |
| author_facet | Frieze, Alan Perez-Gimenez, Xavier |
| contents | We show that w.h.p.\ the random $r$-uniform hypergraph $H_{n,m}$ contains a loose Hamilton cycle, provided $r\geq 3$ and $m\geq \frac{(1+ε)n\log n}{r}$, where $ε$ is an arbitrary positive constant. This is asymptotically best possible, as if $m\leq \frac{(1-ε)n\log n}{r}$ then w.h.p.\ $H_{n,m}$ contains isolated vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05121 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The threshold for loose Hamilton cycles in random hypergraph Frieze, Alan Perez-Gimenez, Xavier Combinatorics We show that w.h.p.\ the random $r$-uniform hypergraph $H_{n,m}$ contains a loose Hamilton cycle, provided $r\geq 3$ and $m\geq \frac{(1+ε)n\log n}{r}$, where $ε$ is an arbitrary positive constant. This is asymptotically best possible, as if $m\leq \frac{(1-ε)n\log n}{r}$ then w.h.p.\ $H_{n,m}$ contains isolated vertices. |
| title | The threshold for loose Hamilton cycles in random hypergraph |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.05121 |