Loose paths in random ordered hypergraphs
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917379168010240 |
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| author | Dudek, Andrzej Frieze, Alan Pegden, Wesley |
| author_facet | Dudek, Andrzej Frieze, Alan Pegden, Wesley |
| contents | We consider the length of {\em ordered loose paths} in the random $r$-uniform hypergraph $H=H^{(r)}(n, p)$. A ordered loose path is a sequence of edges $E_1,E_2,\ldots,E_\ell$ where $\max\{j\in E_i\}=\min\{j\in E_{i+1}\}$ for $1\leq i<\ell$. We establish fairly tight bounds on the length of the longest ordered loose path in $H$ that hold with high probability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12196 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Loose paths in random ordered hypergraphs Dudek, Andrzej Frieze, Alan Pegden, Wesley Combinatorics We consider the length of {\em ordered loose paths} in the random $r$-uniform hypergraph $H=H^{(r)}(n, p)$. A ordered loose path is a sequence of edges $E_1,E_2,\ldots,E_\ell$ where $\max\{j\in E_i\}=\min\{j\in E_{i+1}\}$ for $1\leq i<\ell$. We establish fairly tight bounds on the length of the longest ordered loose path in $H$ that hold with high probability. |
| title | Loose paths in random ordered hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2504.12196 |