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arXiv · 2603.24627

Two-color Ramsey lower bounds for bounded degree hypergraphs

Chunchao Fan·Qizhong Lin
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Abstract

We consider Ramsey numbers of bounded-degree uniform hypergraphs. In particular, we prove that for every $k\ge3$, there exists a constant $c_k>0$ such that, for all sufficiently large $Δ$ and every $n\ge2^Δ$, there is a $k$-uniform $n$-vertex hypergraph $H$ with maximum degree at most $Δ$ satisfying \[ r(H)\ge \tw_{k-1}\!\bigl(c_kΔ\log\logΔ\bigr)\,n. \] Here $\tw_j$ denotes the tower function of height $j$. This constitutes the first progress towards a problem posed by Conlon, Fox and Sudakov.

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Chunchao Fan, Qizhong Lin. 2026-09-13. Two-color Ramsey lower bounds for bounded degree hypergraphs. https://arxiv.org/abs/2603.24627

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