On matroids of branch-width three
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 infinite 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 finite list of excluded minors. © 2002 Elsevier Science (USA).
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Hall, R., Oxley, J., Semple, C., & Whittle, G. (2002). On matroids of branch-width three. Journal of Combinatorial Theory. Series B, 86 (1), 148-171. https://doi.org/10.1006/jctb.2002.2120