BOUNDING THE VERTEX COVER NUMBER OF A HYPERGRAPH

For a hypergraph H, we denote by (i) tau(H) the minimum k such that some set of k vertices meets all the edges, (ii) nu(H) the maximum k such that some k edges are pairwise disjoint, and (iii) A(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 tau(H) is bounded above by a function of nu(H) and lambda(H), and indeed that if lambda\(H) is bounded by a constant then tau(H) is at most a polynomial function of nu(H).