Non-binary matroids having four non-binary elements

An element e of a matroid M is called non-binary when M\e and M/e are both non-binary matroids. Oxley in [6] gave a characterization of the 3-connected non-binary matroids without non-binary elements. In [4], we constructed all the 2-connected matroids having exactly 1, 2 or 3 non-binary elements. In this paper, we will give a characterization of the 3-connected matroids having exactly four non-binary elements.