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arXiv · 2604.23986

A double-exponential lower bound for $r_4(5,n)$

Longma Du·Xinyu Hu·Ruilong Liu·Guanghui Wang
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Abstract

The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. We prove that $r_4(5,n)\ge 2^{2^{cn^{1/7}}}$, where $c>0$ is an absolute constant. As a consequence, we determine the tower growth rate of $r_k(k+1,n)$, which completely solves the problem of establishing the tower growth rate for all classical off-diagonal hypergraph Ramsey numbers, first posed by Erdős and Hajnal in 1972.

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Longma Du, Xinyu Hu, Ruilong Liu, Guanghui Wang. 2026-04-27. A double-exponential lower bound for $r_4(5,n)$. https://arxiv.org/abs/2604.23986

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