On matroids of branch-width three

Authors:
Rhiannon Hall;James Oxley;Charles Semple;Geoff Whittle
Affiliations:
Mathematical Institute, Oxford OX1 3LB, UK;Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana;Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand;School of Mathematical and Computing Sciences, Victoria University, Wellington, New Zealand
Venue:
Journal of Combinatorial Theory Series B
Year:
2002

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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 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.