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arXiv · 0902.0198

Excluding Kuratowski graphs and their duals from binary matroids

Dillon Mayhew·Gordon Royle·Geoff Whittle
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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 some 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 the subset. 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.

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Dillon Mayhew, Gordon Royle, Geoff Whittle. 2009-02-02. Excluding Kuratowski graphs and their duals from binary matroids. https://arxiv.org/abs/0902.0198

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