Mathematics and Statistics

On matroids of branch-width three

Rhiannon Hall, James Oxley, Charles Semple, and Geoff Whittle

View Report [PDF - 252 KB]

Abstract

For all positive integers k, the class B_k of matroids of branch-width at most k is minor-closed. When k is 1 or 2, the class B_k 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.

Back to Research Reports