Document Type
Article
Publication Date
11-1-2023
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 U2,5- or U3,5-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.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory Series B
First Page
133
Last Page
218
Recommended Citation
Brettell, N., Oxley, J., Semple, C., & Whittle, G. (2023). The excluded minors for 2- and 3-regular matroids. Journal of Combinatorial Theory Series B, 163, 133-218. https://doi.org/10.1016/j.jctb.2023.08.003