A characterization of matroidal families of multigraphs

Abstract

Matroidal families were introduced by Simões-Pereira [5]. Although we know uncountably many matroidal families of simple graphs and infinitely many matroidal families with multigraphs as members, it is an open question how one can find all matroidal families.In this paper we give a solution of this problem by certain submodular functions on the set of all finite graphs characterizing the families of connected graphs being matroidal families.