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 $\Delta$ and every $n\ge2^\Delta$, there is a $k$-uniform $n$-vertex hypergraph $H$ with maximum degree at most $\Delta$ satisfying \[
r(H)\ge \tw_{k-1}\!\bigl(c_k\Delta\log\log\Delta\bigr)\,n. \] Here $\tw_j$ denotes the tower function of height $j$. This constitutes the first progress towards a problem posed by Conlon, Fox and Sudakov.
From: Qizhong Lin [view email]
[v1]
Wed, 25 Mar 2026 03:00:54 UTC (13 KB)
[v2]
Sun, 13 Sep 2026 01:51:43 UTC (22 KB)
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