Extremal bi-Helly families

Research output: Contribution to journalConference article

8 Citations (Scopus)

Abstract

A hypergraph (finite set system) ℋ is called a bi-Helly family if it satisfies the following property: if any two edges of a subhypergraph ℋl ⊆ ℋ share at least two vertices, then |∩H∈ℋlH|≥2. Solving a problem raised by Voloshin, we prove that the maximum number of edges in a bi-Helly family of given order n and given edge size r≥5 equals (n-2r-2). For r = 3 we show that the maximum equals the Turán number ex(n; script K sign34 - e) (its determination is a famous open problem in extremal hypergraph theory), and for r = 4 we prove the lower and upper bounds n3/26 and n3/20, respectively. Analogous results are presented under the requirement that each pairwise k-intersecting subhypergraph has k universal common elements.

Original languageEnglish
Pages (from-to)321-331
Number of pages11
JournalDiscrete Mathematics
Volume213
Issue number1-3
DOIs
Publication statusPublished - Feb 28 2000
EventSelected Topics in Discrete Mathematics - Warsaw, Poland
Duration: Aug 26 1996Sep 28 1996

Keywords

  • Extremal problem
  • Helly property
  • Hypergraph
  • Pairwise k-intersecting

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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