Supersaturated graphs and hypergraphs

We shall consider graphs (hypergraphs) without loops and multiple edges . Let Ybe a family of so called prohibited graphs and ex (n, Y) denote the maximum number of edges (hyperedges) a graph (hypergraph) on n vertices can have without containing subgraphs from Y A graph (hypergraph) will be called supersaturated if it has more edges than ex (n, Y). If G has n vertices and ex (n, Y)=k edges (hyperedges), then it always contains prohibited subgraphs . The basic question investigated here is : At least how many copies of L E Y must occur in a graph G" on n vertices with ex (n, Y)+k edges (hyperedges) ?