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COMBINATORICS
2002

On the Excluded Minors for Matroids of Branch-Width Three

10 years 11 months ago
On the Excluded Minors for Matroids of Branch-Width Three
Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. It has been shown in [R. Hall, J. Oxley, C. Semple, G. Whittle, On Matroids of Branch-Width Three, submitted 2001] that if M is an excluded minor for matroids of branch-width 3, then M has at most 14 elements. We show that there are exactly 10 such binary matroids M (7 of which are regular), proving a conjecture formulated by Dharmatilake in 1994. We also construct numbers of such ternary and quaternary matroids M, and provide a simple practical algorithm for finding a width-3 branch-decomposition of a matroid. The arguments in our paper are computer-assisted -- we use a program Macek [P. Hlinen
Petr Hlinený
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2002
Where COMBINATORICS
Authors Petr Hlinený
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