Erdős and Rényi Conjecture

Affirming a conjecture of Erdős and Rényi we prove that for any (real number)c1>0 for somec2>0, if a graphGhas noc1(log n) nodes on which the graph is complete or edgeless (i.e.,Gexemplifies |G|↛(c1 log n)22), thenGhas at least 2c2nnon-isomorphic (induced) subgraphs.