Induced subgraphs of given sizes

Paul Erdos, Zoltán Füredi, Bruce L. Rothschild, Vera T. Sós

Research output: Contribution to journalArticle

1 Citation (Scopus)


We say (n, e) → (m, f), an (m, f) subgraph is forced, if every n-vertex graph of size e has an m-vertex spanned subgraph with f edges. For example, as Turán proved, (n, e) → (k, (k2)) for e > tk-1 (n) and (n, e) → (k, (k2)), otherwise. We give a number of constructions showing that forced pairs are rare. Using tools of extremal graph theory we also show infinitely many positive cases. Several problems remain open.

Original languageEnglish
Pages (from-to)61-77
Number of pages17
JournalDiscrete Mathematics
Issue number1-3
Publication statusPublished - Apr 6 1999


  • Density
  • Ramsey's theorem
  • Turán's theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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