Partition of C 4-Designs into Minimum and Maximum Number of P 3-Designs

Let C be a C4-design of order n and index λ, on the vertex set V , |V | = n. If V1∪· · ·∪Vm = V is a partition of the vertex set, such that the intersections of the C ∈ C with Vi form a P3-design of order |Vi| 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. AMS classification: 05B05.