The transversal numberτ(H) of a hypergraphH is the minimum cardinality of a set of vertices that intersects all edges ofH. Fork ≥ 1 definec k =sup τ(H)/(m + n), whereH ranges over allk-uniform hypergraphs withn vertices andm edges. Applying probabilistic arguments we show thatc k = (1 +o(1))log e k/k. This settles a problem of Tuza.
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Research supported in part by Allon Fellowship and by a grant from the Bat Sheva de Rothschild Foundation.