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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 |
URI: | http://www.sciencedirect.com/science/article/pii/S0095895611000049 http://bura.brunel.ac.uk/handle/2438/7064 |
DOI: | http://dx.doi.org/10.1016/j.jctb.2010.12.004 |
ISSN: | 0095-8956 |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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