The Ramsey number

For two given graphs G 1 and G 2 , the Ramsey number R ( G 1 , G 2 ) is the smallest integer n such that for any graph G of order n , either G contains G 1 or the complement of G contains G 2 . Let C m denote a cycle of length m and K n a complete graph of order n . We show that R ( C 8 , K 8 ) = 50 .