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On the excluded minors for the matroids of branch-width \(k\). (English) Zbl 1032.05027
In [N. Robertson and P. D. Seymour, J. Comb. Theory, Ser. B 52, 153-190 (1991; Zbl 0764.05069)], branch-width was introduced as a parameter for graphs and matroids. The present authors prove that the excluded minors for the class of matroids of branch-width \(k\) have size at most \((6^k-1)/5\).

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
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[1] Geelen, J.F.; Gerards, A.M.H.; Whittle, G.P., Branch-width and well-quasi-ordering in matroids and graphs, J. combin. theory ser. B, 84, 270-290, (2001) · Zbl 1037.05013
[2] Hall, R.; Oxley, J.G.; Semple, C.A.; Whittle, G.P., On the matroids of branch-width 3, J. combin. theory ser. B, 86, 148-171, (2002) · Zbl 1034.05011
[3] Oxley, J.G., Matroid theory, (1992), Oxford University Press New York
[4] Robertson, N.; Seymour, P.D., Graph minors X: obstructions to tree-decomposition, J. combin. theory ser. B, 51, 153-190, (1991) · Zbl 0764.05069
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