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A Bound of the Cardinality of Families not Containing Δ-Systems

  • A. V. Kostochka
Part of the Algorithms and Combinatorics book series (AC, volume 14)

Summary

P. Erdős and R. Rado defined a Δ-system as a family in which every two members have the same intersection. Here we obtain a new upper bound of the maximum cardinality φ(n) of an n-uniform family not containing any Δ-system of cardinality 3. Namely, we prove that for any α > 1, there exists C = C(α) such that for any n, φ(n) ≤ C nn .

Keywords

Greedy Algorithm Extremal Problem Minimum Cardinality Maximum Cardinality Preliminary Lemma 
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References

  1. 1.
    P.Erdős, Problems and results on set systems and hypergraphs, Extended Abstrect, Conf.on Extremal Problems for Finite Sets, 1991, Visegrad, Hungary 1991, 85–92.Google Scholar
  2. 2.
    P.Erdős and R.Rado, Intersection theorems for systems of sets, J.London Math. Soc. 35(1960), 85–90.MathSciNetCrossRefGoogle Scholar
  3. 3.
    J.Spencer, Intersection theorems for systems of sets, Canad. Math. Bull. 20(1977), 249–254.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • A. V. Kostochka
    • 1
  1. 1.Institute of MathematicsSiberian Branch, Russian Academy of SciencesRussia

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