The excluded minors for 2- and 3-regular matroids
| Autor: | Brettell, Nick, Oxley, James, Semple, Charles, Whittle, Geoff |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Journal of Combinatorial Theory, Series B, 163 (2023), 133-218 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jctb.2023.08.003 |
| Popis: | 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. Comment: 79 pages, 1 figure |
| Databáze: | arXiv |
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