Bounding the vertex cover number of a hypergraph

For a hypergraph H, we denote by (i) τ(H) the minimum k such that some set of k vertices meets all the edges, (ii) ν(H) the maximum k such that some k edges are pairwise disjoint, and (iii) λ(H) the maximum k≥2 such that the incidence matrix of H has as a submatrix the transpose of the incidence matrix of the complete graph K_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).