Extremal problems concerning Kneser graphs

P. Frankl, Z. Füredi

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Let A and B be two intersecting families of k-subsets of an n-element set. It is proven that |A ∪ B| ≤ (k-1n-1) + (k-1n-1) holds for n> 1 2(3+ 5)k, and equality holds only if there exist two points a, b such that {a, b} ∩ F ≠ ∅ for all F ∈ A ∪ B. For n = 2k + o( k) an example showing that in this case max |A ∪ B| = (1-o(1))(kn) is given. This disproves an old conjecture of Erdös [7]. In the second part we deal with several generalizations of Kneser's conjecture.

Original languageEnglish
Pages (from-to)270-284
Number of pages15
JournalJournal of Combinatorial Theory, Series B
Volume40
Issue number3
DOIs
Publication statusPublished - Jun 1986

ASJC Scopus subject areas

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

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