Templates for Binary Matroids
Combinatorics
2020-06-02 v2
Abstract
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). Our main result applies to all highly-connected matroids in a class, not just those of maximum size. As a second application, we characterize the highly-connected 1-flowing matroids.
Keywords
Cite
@article{arxiv.1605.08098,
title = {Templates for Binary Matroids},
author = {Kevin Grace and Stefan H. M. van Zwam},
journal= {arXiv preprint arXiv:1605.08098},
year = {2020}
}