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

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