### Abstract

Let script C sign be a C_{4}-design of order n and index λ, on the vertex set V, |V| = n. If V_{1} ∪⋯∪ V_{m} = V is a partition of the vertex set, such that the intersections of the C ε script C sign with V_{i} form a P_{3}-design of order |V_{i}| and the same index λ, for each 1 ≤ i ≤ m, then 2 ≤ m ≤ log_{3}(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.

Original language | English |
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Pages (from-to) | 531-540 |

Number of pages | 10 |

Journal | Graphs and Combinatorics |

Volume | 20 |

Issue number | 4 |

DOIs | |

Publication status | Published - Nov 1 2004 |

### Keywords

- Cycle system
- Embedding
- Path design

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

## Fingerprint Dive into the research topics of 'Partition of C<sub>4</sub>-designs into minimum and maximum number of P<sub>3</sub>-designs'. Together they form a unique fingerprint.

## Cite this

Quattrocchi, G., & Tuza, Z. (2004). Partition of C

_{4}-designs into minimum and maximum number of P_{3}-designs.*Graphs and Combinatorics*,*20*(4), 531-540. https://doi.org/10.1007/s00373-004-0582-z