On matroids of branch-width three

Abstract

For all positive integers k, the class Bk of matroids of branch-width at most k is minor-closed. When k is 1 or 2, the class Bk is, respectively, the class of direct sums of loops and coloops, and the class of direct sums of series- parallel networks. B3 is a much richer class as it contains infnite antichains of matroids and is thus not well-quasi-ordered under the minor order. In this paper, it is shown that, like B₁ and B₂, the class B₃ can be characterized by a nite list of excluded minor