, Volume 3, Issue 2, pp 181–192 | Cite as

Supersaturated graphs and hypergraphs

  • Paul Erdős
  • Miklós Simonovits


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)?

AMS subject classification (1980)

05 C 35 05 C 65 


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Copyright information

© Akadémiai Kiadó 1983

Authors and Affiliations

  • Paul Erdős
    • 1
  • Miklós Simonovits
    • 1
  1. 1.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary

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