Let M be a 3-connected matroid that is not a wheel or a whirl. In this paper, we prove that M has an element e such that M\e or M/e is 3-connected and has no 3-separation that is not equivalent to one induced by M. © 2011 Elsevier Inc.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Oxley, J., Semple, C., & Whittle, G. (2012). An upgraded Wheels-and-Whirls Theorem for 3-connected matroids. Journal of Combinatorial Theory. Series B, 102 (3), 610-637. https://doi.org/10.1016/j.jctb.2011.09.005