Let M be a matroid. When M is 3-connected, Tutte's Wheels-and-Whirls Theorem proves that M has a 3-connected proper minor N with |E(M)-E(N)|=1 unless M is a wheel or a whirl. This paper establishes a corresponding result for internally 4-connected binary matroids. In particular, we prove that if M is such a matroid, then M has an internally 4-connected proper minor N with |E(M)-E(N)|≤3 unless M or its dual is the cycle matroid of a planar or Möbius quartic ladder, or a 16-element variant of such a planar ladder. © 2011 Elsevier Inc.
Publication Source (Journal or Book title)
Journal of Combinatorial Theory. Series B
Chun, C., Mayhew, D., & Oxley, J. (2011). A chain theorem for internally 4-connected binary matroids. Journal of Combinatorial Theory. Series B, 101 (3), 141-189. https://doi.org/10.1016/j.jctb.2010.12.004