### Abstract

Let G be a vertex-disjoint union of directed cycles in the complete directed graph D_{t}, let | E (G) | be the number of directed edges of G and suppose G ≠ over(C, ⇀)_{2} ∪ over(C, ⇀)_{3} or over(C, ⇀)_{5} if t = 5, and G ≠ over(C, ⇀)_{3} ∪ over(C, ⇀)_{3} if t = 6. It is proved in this paper that for each positive integer t, there exist over(C, ⇀)_{3}-decompositions for D_{t} - G if and only if t (t - 1) - | E (G) | ≡ 0 (mod 3).

Original language | English |
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Pages (from-to) | 4705-4715 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 309 |

Issue number | 14 |

DOIs | |

State | Published - 28 Jul 2009 |

### Keywords

- Complete directed graph
- Mendelsohn triples
- Packing

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## Cite this

Pu, L., Fu, H-L., & Shen, H. (2009). Directed 3-cycle decompositions of complete directed graphs with quadratic leaves.

*Discrete Mathematics*,*309*(14), 4705-4715. https://doi.org/10.1016/j.disc.2008.05.039