Lower bounds for small diagonal ramsey numbers

Abstract Let p = 4 r + 1 be a prime. Let G be the graph on the p points 0, 1,…, p −1 formed by connecting two points with an edge iff their difference is a quadratic residue mod p . Let k be the size of the largest clique contained in G . Then it is well known that the diagonal Ramsey number R 2 ( k + 1) > p . We show R 2 ( k + 2) > 2 p + 2. We also compute k for all p