Tangles, tree-decompositions and grids in matroids

J.F. Geelen, B. Gerards, G. Whittle

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)
1 Downloads (Pure)

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 languageEnglish
Pages (from-to)657-667
JournalJournal of Combinatorial Theory, Series B
Volume99
Issue number4
DOIs
Publication statusPublished - 2009

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