Upper bounds of Ramsey numbers

Abstract

For positive integers s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. A widely known theorem, proved by Erdös, state that. In this paper, we improve the upper bounds for R(s, t). That is, we find that.