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On the number of edges in a uniform hypergraph with a range of permitted intersections

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Abstract

The paper studies the quantity p(n, k, t 1, t 2) equal to the maximum number of edges in a k-uniform hypergraph with the property that the size of the intersection of any two edges lies in the interval [t 1, t 2]. Previously known upper and lower bounds are given. New bounds for p(n, k, t 1, t 2) are obtained, and the relationship between these bounds and known estimates is studied. For some parameter values, the exact values of p(n, k, t 1, t 2) are explicitly calculated.

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Authors and Affiliations

  1. Mechanics and Mathematics Faculty, Moscow State University, Moscow, 119991, Russia

    A. V. Bobu, A. E. Kupriyanov & A. M. Raigorodskii

  2. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow oblast, 141700, Russia

    A. M. Raigorodskii

  3. Institute of Mathematics and Computer Science, Buryat State University, Ulan-Ude, Buryat Republic, 670000, Russia

    A. M. Raigorodskii

Authors
  1. A. V. Bobu
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  2. A. E. Kupriyanov
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  3. A. M. Raigorodskii
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Correspondence to A. M. Raigorodskii.

Additional information

Original Russian Text © A.V. Bobu, A.E. Kupriyanov, A.M. Raigorodskii, 2017, published in Doklady Akademii Nauk, 2017, Vol. 475, No. 4, pp. 365–368.

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Bobu, A.V., Kupriyanov, A.E. & Raigorodskii, A.M. On the number of edges in a uniform hypergraph with a range of permitted intersections. Dokl. Math. 96, 354–357 (2017). https://doi.org/10.1134/S1064562417040160

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  • DOI: https://doi.org/10.1134/S1064562417040160

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