Weakly union-free twofold triple systems |
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| Authors: | Yeow Meng Chee Charles J Colbourn Alan C H Ling |
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| Institution: | (1) Department of Computer Science, University of Waterloo, N2L 3G1 Waterloo, Ontario, Canada;(2) Department of Computer Science and Electrical Engineering, University of Vermont, 05405 Burlington, VT, USA;(3) Department of Mathematics and Statistics, University of Vermont, 05405 Burlington, VT, USA |
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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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| Keywords: | 05D05 05C65 05B07 |
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