A characterization of a class of non-binary matroids
A well-known result of \textit{W. T. Tutte} [Trans. Am. Math. Soc. 88, 144- 174 (1958; Zbl 0081.173)] is that the 4-point line is the only non-binary matroid such that, for every element e, both \(M\setminus e\) and M/e, the deletion and contraction of e from M, are binary. This paper characterizes those non-binary matroids M such that, for every element e, \(M\setminus e\) or M/e is binary. In particular, the main result proves that a 3-connected non-binary matroid whose rank and corank exceed two has the specified property if and only if it can be obtained from a 3- connected binary matroid by declaring a circuit-hyperplane of the latter to be independent.
scientific article; zbMATH DE number 4075082