Exact solution of some Turán-type problems

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

Fifteen years ago Chvátal conjectured that if F is a family of k subsets of an n-set, |F|>( n-1 k-1), d is an arbitrary integer with d ≤ k - 1 and (d + 1) k ≤ dn, then there exist d + 1 sets in F with empty intersection such that the intersection of any d of them is non-empty. The validity of this conjecture is established for n ≥ n0(k), in a more general framework. Another problem which is solved asymptotically is when the excluded configuration is a fixed sunflower.

Original languageEnglish
Pages (from-to)226-262
Number of pages37
JournalJournal of Combinatorial Theory, Series A
Volume45
Issue number2
DOIs
Publication statusPublished - Jul 1987

ASJC Scopus subject areas

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

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