### Abstract

For each odd m≥3, we completely solve the problem of when an m-cycle system of order u can be embedded in an m-cycle system of order v, barring a finite number of possible exceptions. In cases where u is large compared to m, where m is a prime power, or where m≤15, the problem is completely resolved. In other cases, the only possible exceptions occur when v-u is small compared to m. This result is proved as a consequence of a more general result that gives necessary and sufficient conditions for the existence of an m-cycle decomposition of a complete graph of order v with a hole of size u in the case where u≥m-2 and v-u≥m+1 both hold.

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

Pages (from-to) | 308-335 |

Number of pages | 28 |

Journal | Journal of Combinatorial Designs |

Volume | 24 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2016 |

### Keywords

- cycle system
- Doyen-Wilson theorem
- graph decomposition
- subsystem

## Cite this

*Journal of Combinatorial Designs*,

*24*(7), 308-335. https://doi.org/10.1002/jcd.21431