A decomposition theory for matroids. III. Decomposition conditions
Journal of Combinatorial Theory Series B
A characterization of a class of non-binary matroids
Journal of Combinatorial Theory Series B
A decomposition theory for matroids VI: almost regular matroids
Journal of Combinatorial Theory Series B
A characterization of the matroids representable over GF(3) and the rationals
Journal of Combinatorial Theory Series B
Inequivalent representations of ternary matroids
Discrete Mathematics
On inequivalent representations of matroids over finite fields
Journal of Combinatorial Theory Series B
Regular Article: Partial Fields and Matroid Representation
Advances in Applied Mathematics
Regular Article: Weak Maps and Stabilizers of Classes of Matroids
Advances in Applied Mathematics
Stabilizers of classes of representable matroids
Journal of Combinatorial Theory Series B
The excluded minors for GF(4)-representable matroids
Journal of Combinatorial Theory Series B
Matroid 4-connectivity: a deletion-contraction theorem
Journal of Combinatorial Theory Series B
Branch-width and Rota's conjecture
Journal of Combinatorial Theory Series B
Advances in Applied Mathematics - Special issue: Memory of Rodica Simon
Bridging Separations in Matroids
SIAM Journal on Discrete Mathematics
The structure of the 3-separations of 3-connected matroids
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
On Rota's conjecture and excluded minors containing large projective geometries
Journal of Combinatorial Theory Series B
Lifts of matroid representations over partial fields
Journal of Combinatorial Theory Series B
Confinement of matroid representations to subsets of partial fields
Journal of Combinatorial Theory Series B
The excluded minors for near-regular matroids
European Journal of Combinatorics
On two classes of nearly binary matroids
European Journal of Combinatorics
Hi-index | 0.00 |
Fix a matroid N. A matroid M is N-fragile if, for each element e of M, at least one of M@?e and M/e has no N-minor. The Bounded Canopy Conjecture is that all GF(q)-representable matroids M that have an N-minor and are N-fragile have branch width bounded by a constant depending only on q and N. A matroid N stabilizes a class of matroids over a field F if, for every matroid M in the class with an N-minor, every F-representation of N extends to at most one F-representation of M. We prove that, if Rota@?s Conjecture is false for GF(q), then either the Bounded Canopy Conjecture is false for GF(q) or there is an infinite chain of GF(q)-representable matroids, each not stabilized by the previous, each of which can be extended to an excluded minor. Our result implies the previously known result that Rota@?s Conjecture holds for GF(4), and that the classes of near-regular and sixth-roots-of-unity matroids have a finite number of excluded minors. However, the bound that we obtain on the size of such excluded minors is considerably larger than that obtained in previous proofs. For GF(5) we show that Rota@?s Conjecture reduces to the Bounded Canopy Conjecture.