Random Ramsey graphs for the four-cycle

Abstract It is shown that there is a graph L with n vertices and at least n1.36 edges such that it contains neither L 3 nor K 2, 3 but every subgraph with 2n 4 3 (log n) 2 edges contains a C 4 , (n > n O ) . Moreover, chromatic number of G is at least n0.1.