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Weakly union-free twofold triple systems

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Abstract

In this paper, we settle a problem of Frankl and Füredi, which is a special case of a problem of Erdös, determining the maximum number of hyperedges in a 3-uniform hypergraph in which no two pairs of distinct hyperedges have the same union. The extremal case corresponds to the existence of weakly union-free twofold triple systems, which is settled here with six definite and four possible exceptions. An application to group testing is also given.

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Authors and Affiliations

  1. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Yeow Meng Chee

  2. Department of Computer Science and Electrical Engineering, University of Vermont, 05405, Burlington, VT, USA

    Charles J. Colbourn

  3. Department of Mathematics and Statistics, University of Vermont, 05405, Burlington, VT, USA

    Alan C. H. Ling

Authors
  1. Yeow Meng Chee
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  2. Charles J. Colbourn
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  3. Alan C. H. Ling
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In memory of Paul Erdös

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Chee, Y.M., Colbourn, C.J. & Ling, A.C.H. Weakly union-free twofold triple systems. Annals of Combinatorics 1, 215–225 (1997). https://doi.org/10.1007/BF02558476

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  • DOI: https://doi.org/10.1007/BF02558476

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