14 citations · 31 across the 21 of their papers we have counts for
6 papers · 1 filter
The Highly Connected Matroids in Minor-closed Classes
Jim Geelen, Bert Gerards, Geoff Whittle
For any minor-closed class of matroids over a fixed finite field, we state an exact structural characterization for the sufficiently connected matroids in the class. We also state…
On Rota's Conjecture and nested separations in matroids
Shalev Ben-David, Jim Geelen
We prove that for each finite field and integer there exists such that no excluded minor for the class of -representable ma…
The number of lines in a matroid with no -minor
Jim Geelen, Peter Nelson
We show that, if is a prime power at most 5, then every rank- matroid with no -minor has no more lines than a rank- projective geometry over GF. We also g…
Explicit bounds for graph minors
Jim Geelen, Tony Huynh, R. Bruce Richter
Let be a surface with boundary , be a collection of disjoint -paths in , and be a non-separating -path in . We prove that there is…
Representation of matroids with a modular plane
Jim Geelen, Rohan Kapadia
We prove that if M is a vertically 4-connected matroid with a modular flat X of rank at least three, then every representation of M | X over a finite field F extends to a unique F-…
Representability of matroids with a large projective geometry minor
Jim Geelen, Rohan Kapadia
We prove that for each prime power there is an integer such that if is a -connected, representable matroid with a PG-minor and no -minor, then…