Article ID Journal Published Year Pages File Type
5777597 Journal of Combinatorial Theory, Series B 2017 19 Pages PDF
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),M⁎(K3,3),M(K5),M⁎(K5)} that contains either M(K3,3) or M⁎(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
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