Annals of Combinatorics 3 (1999) 43-52

Weakly Union-free Maximum Packings

Charles J. Colbourn

Department of Computer Science, University of Vermont, Burlington, VT 05405, USA

Received August 10, 1998

AMS Subject Classification: 05D05, 05C65, 05B07

Abstract.Frankl and Füredi [11] established that the largest number of 3-subsets of an n-set, for which no four distinct sets A,B,C,D satisfy A ∪ B = C ∪ D, is at most $\lfloor \frac{n(n-1)}{3} \rfloor$. Chee, Colbourn, and Ling [6] established that this upper bound is met with few exceptions when n≡ 0,1 (mod 3). In this paper, it is established that the upper bound is also met with few exceptions when n ≡ 2 (mod 3)

Keywords: union-free hypergraph, two-fold triple system, group testing

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