  A d-interval hypergraph has d disjoint copies of the unit interval as its
vertex set, and each edge is the union of d subintervals, one on each copy.
Extending a classical result of Gallai on the case d = 1, Tardos and Kaiser
used topological tools to bound the ratio between the transversal number and
the matching number in such hypergraphs. We take a dual point of view, and
bound the edge-covering number (namely the minimal number of edges covering the
entire vertex set) in terms of a parameter expressing independence of systems
of partitions of the d unit intervals. The main tool we use is an extension of
the KKM theorem to products of simplices, due to Peleg. Our approach also
yields a new proof of the Tardos-Kaiser result.
