an:05569117
Zbl 1229.05070
Geelen, Jim; Gerards, Bert; Whittle, Geoff
Tangles, tree-decompositions and grids in matroids
EN
J. Comb. Theory, Ser. B 99, No. 4, 657-667 (2009).
00249984
2009
j
05B35 05C70 05C83
branch-width; tangles; tree-decomposition; matroids; graph minors
Summary: A tangle in a matroid is an obstruction to small branch-width. In particular, the maximum order of a tangle is equal to the branch-width. We prove that: (i) there is a tree-decomposition of a matroid that ``displays'' all of the maximal tangles, and (ii) when \(M\) is representable over a finite field, each tangle of sufficiently large order ``dominates'' a large grid-minor. This extends results of Robertson and Seymour concerning Graph Minors.