Note on a problem of M. Talagrand1. Issue 4 (1st July 2014) - DeMarco, B.
Abstract Answering a question of M. Talagrand, we show that there is a fixed L with the following property. For positive integers k≤n and p∈[0, 1], if ℱ is the set of subgraphs of Kn containing at least (nk)p(k2) copies of Kk, then there is a set G of subgraphs of Kn such that (i) each member of ℱ contains a member of G and (ii) ∑S∈G(p/L)|S|≤1/2 (where |S| means number of edges). © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 663–668, 2015