### Abstract

We pose and solve the existence of 2-factorizations of complete graphs and complete bipartite graphs that have the number of cycles per 2-factor varying, called pancomponented. Such 2-factorizations exist for all such graphs. The pancomponented problem requires a slight generalization of the methods used to solve pancyclic 2-factorization problem, by building 2-factors from cyclically generated 1-factors. These two solutions are offered as the basic approaches to constructing the two essential parameters of a 2-factorization: the size and the number of cycles in the 2-factors.

Original language | English (US) |
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Pages (from-to) | 99-112 |

Number of pages | 14 |

Journal | Discrete Mathematics |

Volume | 299 |

Issue number | 1-3 |

DOIs | |

State | Published - Aug 28 2005 |

### Keywords

- 2-Factorization
- Cycle decomposition
- Oberwolfach problem

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## Cite this

Froncek, D., & Stevens, B. (2005). Pancomponented 2-factorizations of complete graphs.

*Discrete Mathematics*,*299*(1-3), 99-112. https://doi.org/10.1016/j.disc.2004.09.014