The number of graphs with large forbidden subgraphs
Abstract
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 H1,...,Hn,... are graphs with chromatic numbers r1,...,rn,... and order o(log n), we dermine asymptotically the number of graphs of order n not containing Hn as a subgraph. We also give similar results for induced subgraphs.
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