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arXiv · 2411.13812

When are off-diagonal hypergraph Ramsey numbers polynomial?

David Conlon·Jacob Fox·Benjamin Gunby·Xiaoyu He·Dhruv Mubayi·Andrew Suk·Jacques Verstraëte·Hung-Hsun Hans Yu
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Abstract

A natural open problem in Ramsey theory is to determine those $3$-graphs $H$ for which the off-diagonal Ramsey number $r(H, K_n^{(3)})$ grows polynomially with $n$. We make substantial progress on this question by showing that if $H$ is tightly connected or has at most two tight components, then $r(H, K_n^{(3)})$ grows polynomially if and only if $H$ is contained in an iterated blowup of an edge.

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David Conlon, Jacob Fox, Benjamin Gunby, Xiaoyu He, Dhruv Mubayi, Andrew Suk, Jacques Verstraëte, Hung-Hsun Hans Yu. 2025-10-29. When are off-diagonal hypergraph Ramsey numbers polynomial?. https://arxiv.org/abs/2411.13812

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