### Abstract

An isomorphic factorisation of a digraph D is a partition of its arcs into mutually isomorphic subgraphs. If such a factorisation of D into exactly t parts exists, then t must divide the number of arcs in D. This is called the divisibility condition. It is shown conversely that the divisibility condition ensures the existence of an isomorphic factorisation into t parts in the case of any complete digraph. The sufficiency of the divisibility condition is also investigated for complete m-partite digraphs. It is shown to suffice when m = 2 and t is odd, but counterexamples are provided when m = 2 and t is even, and when m = 3 and either t = 2 or t is odd.

Original language | English |
---|---|

Pages (from-to) | 279-285 |

Number of pages | 7 |

Journal | Mathematika |

Volume | 25 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1978 |

Externally published | Yes |

## Cite this

*Mathematika*,

*25*(2), 279-285. https://doi.org/10.1112/S0025579300009529