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Title: A chain theorem for internally 4-connected binary matroids
Authors: Chun, C
Mayhew, D
Oxley, J
Keywords: Binary matroid;Internally 4-connected;Chain theorem
Issue Date: 2011
Publisher: Elsevier
Citation: Journal of Combinatorial Theory: Series B, 101(3): 141 - 189, May 2011
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)| at most 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.
Description: This is the post-print version of the Article - Copyright @ 2011 Elsevier
ISSN: 0095-8956
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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