Off-diagonal Ramsey numbers for linear hypergraphs

doi:10.1017/s0963548326100443

Off-diagonal Ramsey numbers for linear hypergraphs

2026-04-01

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DOI：10.1017/s0963548326100443

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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, Fox, Gunby, He, Mubayi, Suk, and Verstra & euml;te 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 $C\gt 0$ , there exists a linear $k$ -uniform hypergraph $H$ for which \begin{equation*} r(H,K_n<^>{(k)}) \geq { extrm {twr}}_{k-2}(2<^>{(\log n)<^>C}). \end{equation*}

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Hypergraph

Ramsey number

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Off-diagonal Ramsey numbers for linear hypergraphs

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