Forbidding just one intersection

Peter Frankl, Zoltán Füredi

Research output: Contribution to journalArticle

47 Citations (Scopus)


Following a conjecture of P. Erdös, we show that if F is a family of k-subsets of and n-set no two of which intersect in exactly l elements then for k ≥ 2l + 2 and n sufficiently large |F| ≤ (k - l - 1n - l - 1) with equality holding if and only if F consists of all the k-sets containing a fixed (l + 1)-set. In general we show |F| ≤ dknmax;{;l,k - l - 1};, where dk is a constant depending only on k. These results are special cases of more general theorems (Theorem 2.1-2.3).

Original languageEnglish
Pages (from-to)160-176
Number of pages17
JournalJournal of Combinatorial Theory, Series A
Issue number2
Publication statusPublished - Jul 1985


ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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