Hypergraph Ramsey numbers with quasipolynomial growth rate
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914400092291072 |
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| author | He, Xiaoyu Nie, Jiaxi Post, Logan Verstraëte, Jacques |
| author_facet | He, Xiaoyu Nie, Jiaxi Post, Logan Verstraëte, Jacques |
| contents | For a 3-uniform hypergraph (3-graph) $F$, let $r(F,n)$ be the smallest $N$ such that any $N$-vertex $F$-free 3-graph has an independent set of size $n$. We construct a $3$-graph $H_2$ with six vertices and five edges such that $r(H_2,n)=n^{Θ(\log n)}$, and a more general family of $3$-graphs $F$ for which $r(F,n)=n^{\log^{Θ(1)}(n)}$. These are the first examples of such Ramsey number known to be neither polynomial nor exponential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16069 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hypergraph Ramsey numbers with quasipolynomial growth rate He, Xiaoyu Nie, Jiaxi Post, Logan Verstraëte, Jacques Combinatorics 05C55, 05D10, 05C65 For a 3-uniform hypergraph (3-graph) $F$, let $r(F,n)$ be the smallest $N$ such that any $N$-vertex $F$-free 3-graph has an independent set of size $n$. We construct a $3$-graph $H_2$ with six vertices and five edges such that $r(H_2,n)=n^{Θ(\log n)}$, and a more general family of $3$-graphs $F$ for which $r(F,n)=n^{\log^{Θ(1)}(n)}$. These are the first examples of such Ramsey number known to be neither polynomial nor exponential. |
| title | Hypergraph Ramsey numbers with quasipolynomial growth rate |
| topic | Combinatorics 05C55, 05D10, 05C65 |
| url | https://arxiv.org/abs/2603.16069 |