Off-Diagonal Ramsey Numbers for Linear Hypergraphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913933139378176 |
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| author | He, Xiaoyu Nie, Jiaxi Wigderson, Yuval Yu, Hung-Hsun Hans |
| author_facet | He, Xiaoyu Nie, Jiaxi Wigderson, Yuval Yu, Hung-Hsun Hans |
| contents | We study off-diagonal Ramsey numbers $r(H, K_n^{(k)})$ of $k$-uniform hypergraphs, where $H$ is a fixed linear $k$-uniform hypergraph and $K_n^{(k)}$ is complete on $n$ vertices. Recently, Conlon et al.\ disproved the folklore conjecture that $r(H, K_n^{(3)})$ always grows polynomially in $n$. In this paper we show that much larger growth rates are possible in higher uniformity. In uniformity $k\ge 4$, we prove that for any constant $C>0$, there exists a linear $k$-uniform hypergraph $H$ for which $$r(H,K_n^{(k)}) \geq \textup{twr}_{k-2}(2^{(\log n)^C}).$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05641 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Off-Diagonal Ramsey Numbers for Linear Hypergraphs He, Xiaoyu Nie, Jiaxi Wigderson, Yuval Yu, Hung-Hsun Hans Combinatorics We study off-diagonal Ramsey numbers $r(H, K_n^{(k)})$ of $k$-uniform hypergraphs, where $H$ is a fixed linear $k$-uniform hypergraph and $K_n^{(k)}$ is complete on $n$ vertices. Recently, Conlon et al.\ disproved the folklore conjecture that $r(H, K_n^{(3)})$ always grows polynomially in $n$. In this paper we show that much larger growth rates are possible in higher uniformity. In uniformity $k\ge 4$, we prove that for any constant $C>0$, there exists a linear $k$-uniform hypergraph $H$ for which $$r(H,K_n^{(k)}) \geq \textup{twr}_{k-2}(2^{(\log n)^C}).$$ |
| title | Off-Diagonal Ramsey Numbers for Linear Hypergraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.05641 |