Size of weakly saturated graphs

Abstract: Let be a hereditary property. Let denote the number of forbidden subgraphs, which are contained in G. A graph G is said to be weakly -saturated, if and the edges of the complement of G can be labelled in such way that for the inequality holds, where and . The minimum possible size of weakly -saturated graphs is denoted by . In this paper we shall investigate some properties of weakly saturated graphs. We provide some estimations for the minimum size of weakly -saturated graphs. [Copyright &y& Elsevier]