### Abstract

A c-hybrid triple system of order v is a decomposition of the complete v-vertex digraph into c cyclic tournaments of order 3 and {Mathematical expression} transitive tournaments of order 3. Hybrid triple systems generalize directed triple systems (c = 0) and Mendelsohn triple systems (c = v(v - 1)/3); omitting directions yields an underlying twofold triple system. The spectrum of v and c for which a c-hybrid triple system of order v exists is completely determined in this paper. Using (cubic) block intersection graphs, we then show that every twofold triple system of order {Mathematical expression} underlies a c-hybrid triple system with {Mathematical expression}. Examples are constructed for all sufficiently large v, for which this maximum is at most {Mathematical expression}. The lower bound here is proved by establishing bounds on F_{i}(n, r), the size of minimum cardinality vertex feedback sets in n-vertex i-connected cubic multigraphs having r repeated edges. We establish that {Mathematical expression}, {Mathematical expression}. These bounds are all tight, and the latter is used to derive the lower bound in the design theoretic problem.

Original language | English (US) |
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Pages (from-to) | 15-28 |

Number of pages | 14 |

Journal | Graphs and Combinatorics |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1989 |

Externally published | Yes |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

*Graphs and Combinatorics*,

*5*(1), 15-28. https://doi.org/10.1007/BF01788655