A New Upper Bound Formula for Two Color Classical Ramsey Numbers

Abstract

The two-color Ramsey number $R(k,l)$ is the smallest integer $p$ such that for any graph $G$ on $p$ vertices either $G$ contains a $K_k$ or $\overline{G}$ contains a $K_l$, where $\overline{G}$ denotes the complement of $G$. A new upper bound formula is given for two-color Ramsey numbers. For example, we get $R(7,9)\le 1713$,
$R(8,10)\le 6090$ etc.