On the Ramsey Number \(R(K_5 – e, K_5 – e) \)

Abstract

Using computer algorithms we found that there exists a unique, up to isomorphism, graph on \(21\) points and \(125\) graphs on \(20\) points for the Ramsey number \(R(K_5 – e, K_5 – e) = 22\). We also construct all graphs on \(n\) points for the Ramsey number \(R(K_4 – e, K_5 – e) = 13\) for all \(n \leq 12\).