Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777597 | Journal of Combinatorial Theory, Series B | 2017 | 19 Pages |
Abstract
We consider some applications of our characterisation of the internally 4-connected binary matroids with no M(K3,3)-minor. We characterise the internally 4-connected binary matroids with no minor in M, where M is a subset of {M(K3,3),Mâ(K3,3),M(K5),Mâ(K5)} that contains either M(K3,3) or Mâ(K3,3). We also describe a practical algorithm for testing whether a binary matroid has a minor in M. In addition we characterise the growth-rate of binary matroids with no M(K3,3)-minor, and we show that a binary matroid with no M(K3,3)-minor has critical exponent over GF(2) at most equal to four.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Dillon Mayhew, Gordon Royle, Geoff Whittle,