For a graph G, let f(G) be the largest integer k for which there exist
two vertex-disjoint induced subgraphs of G each on k vertices, both
inducing the same number of edges. We prove that f(G)≥n/2−o(n) for
every graph G on n vertices. This answers a question of Caro and Yuster.Comment: 25 pages, improved presentation, fixed misprints, European Journal of
Combinatoric