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.
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Supported by MIUR, Italy and CNR-GNSAGA
Also affiliated with the Department of Computer Science, University of Veszprém, Hungary; supported in part by the Hungarian Scientific Research Fund, grant OTKA T-32969
AMS classification: 05B05
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Quattrocchi, G., Tuza, Z. Partition of C4-Designs into Minimum and Maximum Number of P3-Designs. Graphs and Combinatorics 20, 531–540 (2004). https://doi.org/10.1007/s00373-004-0582-z
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DOI: https://doi.org/10.1007/s00373-004-0582-z