A chain theorem for internally 4-connected binary matroids

作者：Chun Carolyn^*; Mayhew Dillon; Oxley James

来源：Journal of Combinatorial Theory - Series B, 2011, 101(3): 141-189.

DOI：10.1016/j.jctb.2010.12.004

• Binary matroid
• Internally 4-connected
• Chain theorem

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 vertical bar E(M) - E(N)vertical bar = 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 vertical bar E(M) - E(N)vertical bar <= 3 unless M or its dual is the cycle matroid of a planar or Mobius quartic ladder, or a 16-element variant of such a planar ladder.

• 出版日期2011-5