Let M be a binary matroid that is internally 4-connected, that is, M is 3-connected, and one side of every 3-separation is a triangle or a triad. Let N be an internally 4-connected proper minor of M. In this paper, we show that M has a proper internally 4-connected minor with an N-minor that can be obtained from M either by removing at most three elements, or by removing some set of elements in an easily described way from one of a small collection of special substructures of M.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Chun, C., Mayhew, D., & Oxley, J. (2016). Towards a splitter theorem for internally 4-connected binary matroids IX: The theorem. Journal of Combinatorial Theory. Series B, 121, 2-67. https://doi.org/10.1016/j.jctb.2016.08.001