On the matroids in which all hyperplanes are binary
In this paper, it is shown that, for a minor-closed class ℳ of matroids, the class of matroids in which every hyperplane is in ℳ is itself minor-closed and has, as its excluded minors, the matroids U1,1 ⊕ N such that N is an excluded minor for ℳ. This result is applied to the class of matroids of the title, and several alternative characterizations of the last class are given.
Publication Source (Journal or Book title)
Kingan, S., & Oxley, J. (1996). On the matroids in which all hyperplanes are binary. Discrete Mathematics, 160 (1-3), 265-271. https://doi.org/10.1016/0012-365X(95)00166-T