A chain theorem for internally 4-connected binary matroids

  • Authors:

  • Carolyn Chun;Dillon Mayhew;James Oxley

  • Affiliations:

  • Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA;School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand;Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2011

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Abstract

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)|=