### Abstract

Let m be a positive integer and let G be a graph. We consider the question: can the edge set E (G) of G be expressed as the union of a set M of matchings of G each of which has size exactly m? If this happens, we say that G is [m]-coverable and we call M an [m]-covering of G. It is interesting to consider minimum[m] -coverings, i.e. [m]-coverings containing as few matchings as possible. Such [m]-coverings will be called excessive[m] -factorizations. The number of matchings in an excessive [m]-factorization is a graph parameter which will be called the excessive[m] -index and denoted by χ_{[m]}^{′}. In this paper we begin the study of this new parameter as well as of a number of other related graph parameters.

Original language | English |
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Pages (from-to) | 276-287 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 310 |

Issue number | 2 |

DOIs | |

State | Published - 28 Jan 2010 |

### Keywords

- Excessive [m]-factorization
- Excessive [m]-index
- [m]-covering

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## Cite this

*Discrete Mathematics*,

*310*(2), 276-287. https://doi.org/10.1016/j.disc.2008.09.031