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 $n\le 12$.