BIMSA >
Research seminar in Discrete Mathematics
Lower bounds for Ramsey numbers of bounded degree hypergraphs
Lower bounds for Ramsey numbers of bounded degree hypergraphs
Organizers
Jie Ma
, Benjamin Sudakov
Speaker
Domagoj Bradac
Time
Tuesday, November 25, 2025 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
We prove that, for all $k \ge 3,$ and any integers $\Delta, n$ with $n \ge \Delta,$ there exists a $k$-uniform hypergraph on $n$ vertices with maximum degree at most $\Delta$ whose $4$-color Ramsey number is at least $\mathrm{tw}_k(c_k \Delta) \cdot n$, for some constant $c_k > 0$, where $\mathrm{tw}$ denotes the tower function. For $k \ge 4,$ this is tight up to the constant $c_k$ and for $k = 3$ it is known to be tight up to a factor of $\log \Delta$ on top of the tower. Our bound extends a well-known result of Graham, R\"{o}dl and Ruci\'{n}ski for graphs and answers a question of Conlon, Fox and Sudakov from 2008. Joint work with Zach Hunter and Benny Sudakov.