Name
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. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.jctb.2007.10.008 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
large grid-minor,matroids,tree-decomposition,branch-width tangles tree-decomposition matroids graph minors,finite field,graph minors,small branch-width,maximum order,branch-width,maximal tangle,tangles,large order,tree decomposition,graph minor | Matroid,Tangle,Discrete mathematics,Graph,Finite field,Combinatorics,Tree decomposition,Matroid partitioning,Graphic matroid,Mathematics,Branch-decomposition | Journal |
Volume | Issue | ISSN |
99 | 4 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
11 | 0.74 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jim Geelen | 1 | 241 | 29.49 |
| Bert Gerards | 2 | 146 | 14.47 |
| Geoff Whittle | 3 | 471 | 57.57 |