  In this note, extending some results of Erdos, Frankl, Rodl, Alexeev,
Bollobas and Thomason we determine asymptotically the number of graphs which do
not contain certain large subgraphs. In particular, if H_1,...,H_n,... are
graphs with chromatic numbers r_1,...,r_n,... and order o(log n), we dermine
asymptotically the number of graphs of order n not containing H_n as a
subgraph. We also give similar results for induced subgraphs.
