Note on a problem of M. Talagrand
Answering a question of M. Talagrand, we show that there is a fixed L with the following property. For positive integers and , if is the set of subgraphs of Kn containing at least copies of Kk, then there is a set of subgraphs of Kn such that (i) each member of contains a member of and (ii) (where means number of edges).  2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 663668, 2015
increasing family threshold fractional and integer optima p-small and weakly p-small