Supersaturated graphs and hypergraphs


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

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Erdős, P., Simonovits, M. Supersaturated graphs and hypergraphs. Combinatorica 3, 181–192 (1983).

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AMS subject classification (1980)

  • 05 C 35
  • 05 C 65