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)


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 .


Greedy Algorithm Extremal Problem Minimum Cardinality Maximum Cardinality Preliminary Lemma 
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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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