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Transversal numbers of uniform hypergraphs

Graphs and Combinatorics volume 6, pages 1–4 (1990)Cite this article

Abstract

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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References

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Authors and Affiliations

  1. Department of Mathematics, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Noga Alon

  2. Bell Communications Research, 07960, Morristown, NJ, USA

    Noga Alon

Authors
  1. Noga Alon
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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). https://doi.org/10.1007/BF01787474

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  • DOI: https://doi.org/10.1007/BF01787474

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