Bounding the vertex cover number of a hypergraph

AbstractFor a hypergraphH, we denote by(i)τ(H) the minimumk such that some set ofk vertices meets all the edges,(ii)ν(H) the maximumk such that somek edges are pairwise disjoint, and(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).