A New Upper Bound Formula for Two Color Classical Ramsey Numbers

Huang Yi Ru1, Zhang Ke Mint 2
1Department of Mathematics Shanghai University Shanghai 201800 P.R. of China
2 Department of Mathematics Nanjing University Nanjing 210008 P.R. of China

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 \(R(7,9) \leq 1713\),
\(R(8,10) \leq 6090\) etc.