KonstantinTikhomirov Archives - Discrete Mathematics Group

A well-known conjecture of Burr and Erdős 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 $r (Q_{n}) = O (2^{2 n - c n})$ for a universal constant $c > 0$ , improving upon the previous best-known bound $r (Q_{n}) = O (2^{2 n})$ , due to Conlon, Fox, and Sudakov.