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 M. 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.

Excessive [l,m]-factorizations / Cariolaro, David; Mazzuoccolo, Giuseppe. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 338:11(2015), pp. 1917-1927. [10.1016/j.disc.2015.04.030]

### Excessive [l,m]-factorizations

#### 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 M. 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.
##### Scheda breve Scheda completa Scheda completa (DC)
2015
338
11
1917
1927
Excessive [l,m]-factorizations / Cariolaro, David; Mazzuoccolo, Giuseppe. - In: DISCRETE MATHEMATICS. - ISSN 0012-365X. - 338:11(2015), pp. 1917-1927. [10.1016/j.disc.2015.04.030]
Cariolaro, David; Mazzuoccolo, Giuseppe
File in questo prodotto:
File
cariolaro_mazzuoccolo_revised_4.pdf

Accesso riservato

Dimensione 325.51 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11380/1310845`