The Ramsey number for a cycle of length six versus a clique of order eight

For two given graphs G1G1 and G2G2, the Ramsey number R(G1,G2)R(G1,G2) is the smallest integer nn such that for any graph GG of order nn, either GG contains G1G1 or the complement of GG contains G2G2. Let CmCm denote a cycle of length mm and KnKn a complete graph of order nn. In this paper, it is shown that R(C6,K8)=36R(C6,K8)=36.