Off-Diagonal Ramsey Numbers for Linear Hypergraphs

2025/07/08 by Xiaoyu He, He, Xiaoyu, Jiaxi Nie +5
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.05641

Abstract

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≥ 4, we prove that for any constant C>0, there exists a linear k-uniform hypergraph H for which r(H,K_n^(k)) ≥ \textuptwr_k-2(2^{(log n)C}).

Citations

• Improving R(3,k) in just two bites
• When are off-diagonal hypergraph Ramsey numbers polynomial?
• On off-diagonal hypergraph Ramsey numbers
• The asymptotics of r(4,t)
• New lower bounds for hypergraph Ramsey numbers
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• Dynamic concentration of the triangle-free process
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• When are off-diagonal hypergraph Ramsey numbers polynomial?