Saturated graphs with minimal number of edges

Let F = {F₁,…} be a given class of forbidden graphs. A graph G is called F-saturated if no F_i ∈ F is a subgraph of G but the addition of an arbitrary new edge gives a forbidden subgraph. In this paper the minimal number of edges in F-saturated graphs is examined. General estimations are given and the structure of minimal graphs is described for some special forbidden graphs (stars, paths, m pairwise disjoint edges).