It is a well-known result of Tutte, A homotopy theorem for matroids, I, II, Trans. Amer. Math. Soc. 88 (1958) 144-174. that U2,4 is the only non-binary matroid M such that, for every element e, both M\e and M/e are binary. Oxley generalized this result by characterizing the non-binary matroids M such that, for every element e of M, the deletion M\e or the contraction M/e is binary. We characterize those non-binary matroids M such that, for all elements e and f, at least two of M\e, f; M\e/f; M/e\f; and M/e, f are binary. © 1999 Elsevier Science B.V. All rights reserved.
Publication Source (Journal or Book title)
Mills, A., & Oxley, J. (1999). A class of non-binary matroids with many binary minors. Discrete Mathematics, 207 (1-3), 173-187. https://doi.org/10.1016/S0012-365X(98)00355-0