We prove that if M is a 4-connected binary matroid and N is an internally 4-connected proper minor of M with at least 7 elements, then, unless M is a certain 16-element matroid, there is an element e of E(M) such that either M\e or M/e is internally 4-connected having an N-minor. This strengthens a result of Zhou and is a first step towards obtaining a splitter theorem for internally 4-connected binary matroids. © 2011 Elsevier Inc.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Chun, C., Mayhew, D., & Oxley, J. (2012). Towards a splitter theorem for internally 4-connected binary matroids. Journal of Combinatorial Theory. Series B, 102 (3), 688-700. https://doi.org/10.1016/j.jctb.2011.08.006