### Abstract

Two theorems are proved in this paper. Firstly, it is proved that there exists a decomposition of the complete graph of order n into t edge-disjoint 2-regular subgraphs of orders m1, m2,..., mt if and only if n is odd, 3a??mia??n for i = 1, 2,..., t, and m1 + m2 + ... + mt = (n/2). Secondly, it is proved that if there exists partial decomposition of the complete graph Kn of order n into t cycles of lengths m1, m2,..., mt, then there exists an equitable partial decomposition of K n into t cycles of lengths m1, m2,..., mt. A decomposition into cycles is equitable if for any two vertices u and v, the number of cycles containing u and the number of cycles containing v differ by at most 1

Original language | English |
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Pages (from-to) | 67 - 72 |

Number of pages | 6 |

Journal | Journal of Combinatorial Theory, Series B |

Volume | 93 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2005 |

Externally published | Yes |

## Cite this

Bryant, D., Horsley, D., & Maenhaut, B. (2005). Decompositions into 2-regular subgraphs and equitable partial cycle decompositions.

*Journal of Combinatorial Theory, Series B*,*93*(1), 67 - 72. https://doi.org/10.1016/j.jctb.2004.06.002