For a graph G, denote by t(G) (resp. b(G)) the maximum size of a triangle-free (resp. bipartite) subgraph of G. Of course t(G) ≥ b(G) for any G, and a classic result of Mantel from 1907 (the first case of Turán's Theorem) says that equality holds for complete graphs. A natural question, first considered by Babai, Simonovits and Spencer about 20 years ago… (More)
Answering a question of Kolaitis and Kopparty, we show that, for given integer q > 1 and pairwise nonisomorphic connected graphs G ξ k) is asymptotically uniformly distributed on Z k q .