Partition of C₄-Designs into Minimum and Maximum Number of P₃-Designs

Abstract.

Let be a C₄-design of order n and index λ, on the vertex set V, |V|=n. If V₁∪⋯∪V _m =V is a partition of the vertex set, such that the intersections of the with V _i form a P₃-design of order |V _i | and the same index λ, for each 1≤i≤m, then 2≤m≤ log₃(2n+1). The minimum bound is best possible for every λ. The maximum bound is best possible for λ=2, and hence also for every even λ.