The minimum number of subgraphs in a graph and its complement
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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 Kn. 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.
[1] Stefan A. Burr,et al. On the Ramsey multiplicities of graphs - problems and recent results , 1980, J. Graph Theory.
[2] A. Goodman. On Sets of Acquaintances and Strangers at any Party , 1959 .
[3] A. Thomason. A Disproof of a Conjecture of Erdős in Ramsey Theory , 1989 .