On matroids of branch-width three

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Journal Article
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University of Canterbury. Mathematics and Statistics.
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Date
2002
Authors
Hall, R.
Oxley, J.
Semple, C.
Whittle, G.
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 minors

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Hall, R., Oxley, J., Semple, C., Whittle, G. (2002) On matroids of branch-width three. Journal of Combinatorial Theory, Series B, 86, pp. 148-171.
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