# zbMATH — the first resource for mathematics

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
##### Keywords:
Branch-width; matroids; connectivity; excluded minors
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.