Disperse Hypergraphs
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916912648159232 |
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| author | Gishboliner, Lior Honest, Ethan |
| author_facet | Gishboliner, Lior Honest, Ethan |
| contents | For $\ell \geq 3$, an $\ell$-uniform hypergraph is disperse if the number of edges induced by any set of $\ell+1$ vertices is 0, 1, $\ell$ or $\ell+1$. We show that every disperse $\ell$-uniform hypergraph on $n$ vertices contains a clique or independent set of size $n^{Ω_{\ell}(1)}$, answering a question of the first author and Tomon. To this end, we prove several structural properties of disperse hypergraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Disperse Hypergraphs Gishboliner, Lior Honest, Ethan Combinatorics For $\ell \geq 3$, an $\ell$-uniform hypergraph is disperse if the number of edges induced by any set of $\ell+1$ vertices is 0, 1, $\ell$ or $\ell+1$. We show that every disperse $\ell$-uniform hypergraph on $n$ vertices contains a clique or independent set of size $n^{Ω_{\ell}(1)}$, answering a question of the first author and Tomon. To this end, we prove several structural properties of disperse hypergraphs. |
| title | Disperse Hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.21052 |