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arXiv · 2206.15188

The excluded minors for 2- and 3-regular matroids

Nick Brettell·James Oxley·Charles Semple·Geoff Whittle
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Abstract

The class of 2-regular matroids is a natural generalisation of regular and near-regular matroids. We prove an excluded-minor characterisation for the class of 2-regular matroids. The class of 3-regular matroids coincides with the class of matroids representable over the Hydra-5 partial field, and the 3-connected matroids in the class with a $U_{2,5}$- or $U_{3,5}$-minor are precisely those with six inequivalent representations over GF(5). We also prove that an excluded minor for this class has at most 15 elements.

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Nick Brettell, James Oxley, Charles Semple, Geoff Whittle. 2023-09-06. The excluded minors for 2- and 3-regular matroids. https://doi.org/10.1016/j.jctb.2023.08.003

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