  Given two positive integers l and m, with l \le 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 \le |L| \le m for every matching L of 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
\infty, 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 \chi'[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 \chi'[l,m](G)
and outputs an excessive [l,m]-factorization of G, whenever the latter exists.
