### Abstract

Conditions for the existence of a 6-cycle system of K_{n}-E(F) for any spanning forest F of K_{n} were discussed. Here, F is a leave and a forest is defined as the graph that contains no cycle. It was shown that when the leave is a forest, it must be that n is even. Results obtaining m-cycle systems of graphs that are close to complete, were obtained when m is odd, with each vertex having even degree in the leave.

Original language | English |
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Pages (from-to) | 27-41 |

Number of pages | 15 |

Journal | Discrete Mathematics |

Volume | 281 |

Issue number | 1-3 |

DOIs | |

State | Published - 28 Apr 2004 |

### Keywords

- 6-cycle
- Cycle systems
- Forest
- Leave

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## Cite this

Ashe, D. J., Fu, H-L., & Rodger, C. A. (2004). A solution to the forest leave problem for partial 6-cycle systems.

*Discrete Mathematics*,*281*(1-3), 27-41. https://doi.org/10.1016/j.disc.2003.08.004