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Graphs and Combinatorics

, Volume 6, Issue 1, pp 1–4 | Cite as

Transversal numbers of uniform hypergraphs

  • Noga Alon
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.

Keywords

Minimum Cardinality Probabilistic Argument Uniform Hypergraphs Transversal Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Bollobás, B.: Random Graphs, p. 319. New York: Academic Press, 1985Google Scholar
  2. 2.
    Graham, R.L., Spencer, J.H.: A constructive solution to a tournament problem. Canad. Math. Bull.14, 45–48 (1971)Google Scholar
  3. 3.
    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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