Let M be a 3-connected matroid other than a wheel or a whirl. In the next paper in this series, we prove that there is an element whose deletion from M or M* is 3-connected and whose only 3-separations are equivalent to those induced by M. The strategy used to prove this theorem involves showing that we can remove some element from a leaf of the tree of 3-separations of M. The main result of this paper is designed to allow us to do this. © 2010 Elsevier Inc.
Publication Source (Journal or Book title)
Advances in Applied Mathematics
Oxley, J., Semple, C., & Whittle, G. (2011). Exposing 3-separations in 3-connected matroids. Advances in Applied Mathematics, 47 (3), 463-508. https://doi.org/10.1016/j.aam.2010.10.009