A chain theorem for internally 4-connected binary matroids |
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Authors: | Carolyn Chun |
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Institution: | a Department of Mathematics, Louisiana State University, Baton Rouge, LA, USA b School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand |
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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)|?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. |
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Keywords: | Binary matroid Internally 4-connected Chain theorem |
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