Random packing by matroid bases and triangles Original Research Article

Let M be a matroid on a finite set E(M). Then M is packable by bases if E(M) is the disjoint union of bases. A partial packing of M is a collection of disjoint bases whose union is a proper subset of E(M). M is a randomly packable by bases if every partial packing can be extended to a packing of M. This paper determines the structure of the matroids that are randomly packable by bases. It also gives a characterization, in terms of forbidden restrictions, of the simple matroids that are randomly packable by 3-circuits.