Abstract
AbstractA (2,3)‐packing on X is a pair (X,$\cal A$), where $\cal A$ is a set of 3‐subsets (called blocks) of X, such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph (X,E) such that E consists of all the pairs which do not appear in any block of $\cal A$. In this article, we shall construct a set of 6k − 2 disjoint (2,3)‐packings of order 6k + 4 with K1,3 ∪ 3kK2 or G1 ∪ (3k − 1)K2 as their common leave for any integer k ≥ 1 with a few possible exceptions (G1 is a special graph of order 6). Such a system can be used to construct perfect threshold schemes as noted by Schellenberg and Stinson (1989). © 2006 Wiley Periodicals, Inc. J Combin Designs
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