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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 529.05027

**Autor: ** Erdös, Paul; Simonovits, Miklos

**Title: ** Supersaturated graphs and hypergraphs. (In English)

**Source: ** Combinatorica 3, 181-192 (1983).

**Review: ** In this paper are investigated supersaturated graphs and hypergraphs. Let *L* be a family of graphs (hypergraphs) and ex (n,*L*) denote the maximum number of edges (hyperedges) of a graph (hypergraph) on n vertices which do not contain a subgraph from *L*. A graph (hypergraph) with n vertices containing more than ex(n,*L*) edges es called a supersaturated graph (hypergraph).

The problem solved in this paper is to determine the number of copies of a subgraph from *L* which must occur in a supersaturated graph (hypergraph) with ex(n,*L*)+k edges. There are given some lower bounds for the number of subgraphs from *L* with respect to value of k. In the case of ordinary graphs the characterisation of supersaturated graphs with a low number of prohibited subgraphs is given.

**Reviewer: ** L.Niepel

**Classif.: ** * 05C35 Extremal problems (graph theory)

05C65 Hypergraphs

**Keywords: ** uniform hypergraph; forbidden subgraphs; Turan graphs; supersaturated hypergraph

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag