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On Matroids of Branch-Width Three

✍ Scribed by Rhiannon Hall; James Oxley; Charles Semple; Geoff Whittle

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 242 KB
Volume: 86
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.2002.2120

No coin nor oath required. For personal study only.

✦ Synopsis

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. B 3 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 B 1 and B 2 ; the class B 3 can be characterized by a finite list of excluded minors.

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