Hypergraph families with bounded edge cover or transversal number

A. Gyárfás, J. Lehel

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The transversal number, packing number, covering number and strong stability number of hypergraphs are denoted by τ, ν, ρ{variant} and α, respectively. A hypergraph family {thorn} is called τ-bound (ρ{variant}-bound) if there exists a "binding function"f(x) such that τ(H)≦f(v(H)) (ρ{variant}(H)≦f(α(H))) for all H ∈ {thorn}. Methods are presented to show that various hypergraph families are τ-bound and/or ρ{variant}-bound. The results can be applied to families of geometrical nature like subforests of trees, boxes, boxes of polyominoes or to families defined by hypergraph theoretic terms like the family where every subhypergraph has the Helly-property.

Original languageEnglish
Pages (from-to)351-358
Number of pages8
JournalCombinatorica
Volume3
Issue number3-4
DOIs
Publication statusPublished - Sep 1 1983

Keywords

  • AMS subject classification (1980): 05C65, 05B40

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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