Abstract
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.
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