Hypergraph families with bounded edge cover or transversal number

Abstract

The transversal number, packing number, covering number and strong stability number of hypergraphs are denoted by τ, ν, ϱ and α, respectively. A hypergraph family þ is called τ-bound (ϱ-bound) if there exists a “binding function”f(x) such that τ(H)≦f(v(H)) (ϱ(H)≦f(α(H))) for allH ∈ þ. Methods are presented to show that various hypergraph families are τ-bound and/or ϱ-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.

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Gyárfás, A., Lehel, J. Hypergraph families with bounded edge cover or transversal number. Combinatorica 3, 351–358 (1983). https://doi.org/10.1007/BF02579191

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AMS subject classification (1980)

  • 05C 65
  • 05 B 40