Size of weakly saturated graphs Original Research Article

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