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Transversal numbers of uniform hypergraphs


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.

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Alon, N. Transversal numbers of uniform hypergraphs. Graphs and Combinatorics 6, 1–4 (1990).

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