A particular class of graphic matroids

Let M = ( E , F ) be a matroid on a set E and B one of its bases. A closed set θ ⊆ E is saturated with respect to B when | θ ∩ B | = r ( θ ) , where r ( θ ) is the rank of θ. llection of subsets I of E such that | I ∩ θ | ⩽ r ( θ ) for every closed saturated set θ turns out to be the family of independent sets of a new matroid on E, called base-matroid and denoted by M B . In this paper we determine a characterization of a matroid M isomorphic to M B , for a given base B of M. We also characterize graphic matroids M which are never isomorphic to M B , for every base B of M.