Let script C sign 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 ε script C sign 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.
- Cycle system
- Path design
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics