On hypergraphs without two edges intersecting in a given number of vertices

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Let X be a finite set of n-melements and suppose t ≥ 0 is an integer. In 1975, P. Erdös asked for the determination of the maximum number of sets in a family F = {F1,..., Fm}, Fi ⊂ X, such that ∥Fi ∩ Fj∥ ≠ t for 1 ≤ i ≠ j ≤ m. This problem is solved for n ≥ n0(t). Let us mention that the case t = 0 is trivial, the answer being 2n - 1. For t = 1 the problem was solved in [3]. For the proof a result of independent interest (Theorem 1.5) is used, which exhibits connections between linear algebra and extremal set theory.

Original languageEnglish
Pages (from-to)230-236
Number of pages7
JournalJournal of Combinatorial Theory, Series A
Volume36
Issue number2
DOIs
Publication statusPublished - Mar 1984

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ASJC Scopus subject areas

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

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