Beyond the Erdős-Ko-Rado theorem

Peter Frankl, Zoltán Füredi

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

The exact bound in the Erdo{combining double acute accent}s-Ko-Rado theorem is known [F, W]. It states that if n ≥ (t + 1)(k - t + 1), and F is a t-intersecting family of k-sets of an n-set (|F ∩ F′| ≥ t for all F, F′ ∈ F),then |F≤( n-1 k-1). Define Ar = {F ⊂ {1, 2, ..., n} : |F| = k, |F ∩ {1, 2, ..., t + 2r}| ≥ t + r}. Here it is proved that for n>c t log(t+1) (k - t + 1) one has |F| ≤ maxr |Ar|.

Original languageEnglish
Pages (from-to)182-194
Number of pages13
JournalJournal of Combinatorial Theory, Series A
Volume56
Issue number2
DOIs
Publication statusPublished - Mar 1991

ASJC Scopus subject areas

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

Fingerprint Dive into the research topics of 'Beyond the Erdős-Ko-Rado theorem'. Together they form a unique fingerprint.

  • Cite this