Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Fan, Chunchao, Lin, Qizhong
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7141660566
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