14 citations · 31 across the 21 of their papers we have counts for
25 papers
A Sylvester-Gallai-type theorem for complex-representable matroids
Jim Geelen, Matthew E. Kroeker
The Sylvester-Gallai Theorem states that every rank- real-representable matroid has a two-point line. We prove that, for each , every complex-representable matroid with…
Excluding a line from -representable matroids
Jim Geelen, Peter Nelson, Zach Walsh
For each positive integer and each sufficiently large integer , we show that the maximum number of elements of a simple, rank-, -representable matroid with no…
Matroid fragility and relaxations of circuit hyperplanes
Jim Geelen, Florian Hoersch
We relate two conjectures that play a central role in the reported proof of Rota's Conjecture. Let be a finite field. The first conjecture states that: the branch-width…
On the complex-representable excluded minors for real-representability
Rutger Campbell, Jim Geelen
We show that each real-representable matroid is a minor of a complex-representable excluded minor for real-representability. More generally, for an infinite field an…
Infinitely many excluded minors for frame matroids and for lifted-graphic matroids
Rong Chen, Jim Geelen
We present infinite sequences of excluded minors for both the class of lifted-graphic matroids and the class of frame matroids.
A generalization of the Grid Theorem
Jim Geelen, Benson Joeris
A graph has tree-width at most if it can be obtained from a set of graphs each with at most vertices by a sequence of clique sums. We refine this definition by, for each…