Graphs and Combinatorics

, Volume 6, Issue 1, pp 1–4 | Cite as

Transversal numbers of uniform hypergraphs

  • Noga Alon


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.


Minimum Cardinality Probabilistic Argument Uniform Hypergraphs Transversal Number 
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    Lai, Feng-Chu, Chang, Gerard J.: An upper bound for the transversal numbers of 4-uniform hypergraphs. (preprint, 1988)Google Scholar
  4. 4.
    Tuza, Z.: Covering all cliques of a graph. (preprint, 1986)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Noga Alon
    • 1
    • 2
  1. 1.Department of Mathematics, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Bell Communications ResearchMorristownUSA

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