The minimum number of subgraphs in a graph and its complement

For a graphb F without isolated vertices, let M(F; n) denote the minimum number of monochromatic copies of F in any 2-coloring of the edges of K_n. Burr and Rosta conjectured that when F has order t, size u, and a automorphisms. Independently, Sidorenko and Thomason have shown that the conjecture is false. We give families of graphs F of order t, of size u, and with a automorphisms where . We show also that the asymptotic value of M(F; n) is not solely a function of the order, size and number of automorphisms of F. © 1929 John Wiley & Sons, Inc.