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Research seminar in Discrete Mathematics
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.