Publications of (and about) Paul Erdös
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.
Classif.: * 05C35 Extremal problems (graph theory)
Keywords: uniform hypergraph; forbidden subgraphs; Turan graphs; supersaturated hypergraph
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