Bounding the vertex cover number of a hypergraph

Abstract

For a hypergraphH, we denote by

  1. (i)

    τ(H) the minimumk such that some set ofk vertices meets all the edges,

  2. (ii)

    ν(H) the maximumk such that somek edges are pairwise disjoint, and

  3. (iii)

    λ(H) the maximumk≥2 such that the incidence matrix ofH has as a submatrix the transpose of the incidence matrix of the complete graphK k .

We show that τ(H) is bounded above by a function of ν(H) and λ(H), and indeed that if λ(H) is bounded by a constant then τ(H) is at most a polynomial function of ν(H).

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Ding, GL., Seymour, P. & Winkler, P. Bounding the vertex cover number of a hypergraph. Combinatorica 14, 23–34 (1994). https://doi.org/10.1007/BF01305948

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AMS subject classification codes (1991)

  • 05 C 65
  • 05 C 35