Abstract
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.
Original language | English |
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Pages (from-to) | 657-667 |
Journal | Journal of Combinatorial Theory, Series B |
Volume | 99 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2009 |