Combinatorica

, Volume 14, Issue 1, pp 23–34

Bounding the vertex cover number of a hypergraph

  • Guo-Li Ding
  • Paul Seymour
  • Peter Winkler
Article

DOI: 10.1007/BF01305948

Cite this article as:
Ding, GL., Seymour, P. & Winkler, P. Combinatorica (1994) 14: 23. doi:10.1007/BF01305948

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 graphKk.

     

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).

AMS subject classification codes (1991)

05 C 65 05 C 35 

Copyright information

© Akadémiai Kiadó - Springer-Verlag 1994

Authors and Affiliations

  • Guo-Li Ding
    • 1
  • Paul Seymour
    • 2
  • Peter Winkler
    • 2
  1. 1.Department of MathematicsLouisiana State UniversityBaton Rouge
  2. 2.BellcoreMorristown

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