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arXiv · 1501.00327

Towards a splitter theorem for internally 4-connected binary matroids VIII: small matroids

Carolyn Chun·Dillon Mayhew·James Oxley
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Abstract

Our splitter theorem for internally 4-connected binary matroids studies pairs of the form (M,N), where N and M are internally 4-connected binary matroids, M has a proper N-minor, and if M' is an internally 4-connected matroid such that M has a proper M'-minor and M' has an N-minor, then |E(M)|-|E(M')|>3. The analysis in the splitter theorem requires the constraint that |E(M)|>15. In this article, we complement that analysis by using an exhaustive computer search to find all such pairs satisfying |E(M)|<16.

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Carolyn Chun, Dillon Mayhew, James Oxley. 2016-07-12. Towards a splitter theorem for internally 4-connected binary matroids VIII: small matroids. https://arxiv.org/abs/1501.00327

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