The ACO Seminar (2022–2023)

January 26, 3:30pm, Wean 8220
Konstantin Tikhomirov, Carnegie Mellon University
A remark on the Ramsey number of the hypercube

Abstract:

A well known conjecture of Burr and Erdos asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that $r(Q_n)=O(2^{2n−cn})$ for a universal constant $c>0$, improving upon the previous best known bound $r(Q_n)=O(2^{2n})$, due to Conlon, Fox and Sudakov.