## Abstract

Given two positive integers l and m, with l≤m, an [l,m]-covering of a graph G is a set M of matchings of G whose union is the edge set of G and such that l≤;|M|≤m for every MεM. An [l,m]-covering M of G is an excessive [l,m]-factorization of G if the cardinality of M is as small as possible. The number of matchings in an excessive [l,m]-factorization of G (or ∞, if G does not admit an excessive [l,m]-factorization) is a graph parameter called the excessive [l,m]-index of G and denoted by χ[l,m]′(G). In this paper we study such parameter. Our main result is a general formula for the excessive [l,m]-index of a graph G in terms of other graph parameters. Furthermore, we give a polynomial time algorithm which computes χ[l,m]′(G) for any fixed constants l and m and outputs an excessive [l,m]-factorization of G, whenever the latter exists.

Original language | English |
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Pages (from-to) | 1917-1927 |

Number of pages | 11 |

Journal | Discrete Mathematics |

Volume | 338 |

Issue number | 11 |

DOIs | |

Publication status | Published - 6 Jun 2015 |

Externally published | Yes |

## Keywords

- Chromatic index
- Excessive [ l m ] -factorization
- Excessive [ l m ] -index
- Matching