# Templates for Binary Matroids

@article{Grace2017TemplatesFB, title={Templates for Binary Matroids}, author={Kevin Grace and Stefan H. M. van Zwam}, journal={SIAM J. Discret. Math.}, year={2017}, volume={31}, pages={254-282} }

A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a preorder on these templates and determine the nontrivial templates that are minimal with respect to this order. As an application of our main result, we determine the eventual growth rates of certain minor-closed classes of binary matroids, including the class of binary matroids with no minor isomorphic to PG(3,2…

## 7 Citations

The templates for some classes of quaternary matroids

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. B
- 2021

Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, the highly connected members of the class of golden-mean matroids are completely characterized and this leads to a determination of the eventual extremal functions for these classes.

On The Density of Binary Matroids Without

- 2016

This thesis is motivated by the following question: how many elements can a simple binary matroid with no PG(t, 2)-minor have? This is a natural analogue of questions asked about the density of…

THE TEMPLATES FOR SOME CLASSES OF QUATERNARY

- 2019

Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the class of golden-mean matroids and several…

On Perturbations of Highly Connected Dyadic Matroids

- MathematicsAnnals of Combinatorics
- 2018

AbstractGeelen, Gerards, and Whittle [3] announced the following result:
let $${q = p^k}$$q=pk be a prime power, and let $${\mathcal{M}}$$M be a proper minor-closed class of GF(q)-representable…

The extremal function for geometry minors of matroids over prime fields

- Mathematics
- 2017

For each projective or affine geometry $N$ over a prime field $\mathbb{F}$, we give a best-possible upper bound on number of elements in a simple $\mathbb{F}$-representable matroid $M$ of…

The Highly Connected Even-Cycle and Even-Cut Matroids

- Computer Science, MathematicsSIAM J. Discret. Math.
- 2019

It is shown that the number of excluded minors for these classes can be drastically reduced if in each class only the highly connected matroids of sufficient size are considered.

On the Highly Connected Dyadic, Near-Regular, and Sixth-Root-of-Unity Matroids

- Mathematics, Computer ScienceSIAM J. Discret. Math.
- 2021

Subject to announced results by Geelen, Gerards, and Whittle, the highly connected members of the classes of dyadic, near-regular, and sixth-root-of-unity matroids are characterized.

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