### Abstract

It was proved by Buratti and Del Fra that for each pair of odd integers r and m, there exists a cyclic m-cycle system of the balanced complete r-partite graph K _{r(m)} except for the case when r=m=3. In this note, we study the existence of a cyclic m-cycle system of K _{r(m)} where r or m is even. Combining the work of Buratti and Del Fra, we prove that cyclic m-cycle systems of K _{r(m)} exist if and only if (a) K _{r(m)} is an even graph (b) (r, m) ≠ (3, 3) and (c) (r,m) ≢ (t , 2) (mod 4) where t ∈ {2,3}.

Original language | English |
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Pages (from-to) | 427-432 |

Number of pages | 6 |

Journal | Graphs and Combinatorics |

Volume | 22 |

Issue number | 3 |

DOIs | |

State | Published - 1 Nov 2006 |

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## Cite this

Wu, S. L., & Fu, H-L. (2006). A note on cyclic m-cycle systems of K r(m).

*Graphs and Combinatorics*,*22*(3), 427-432. https://doi.org/10.1007/s00373-006-0658-z