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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/7064

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
Publication 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
Sponsorship: This study was partially supported by the National Security Agency.
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:School of Information Systems, Computing and Mathematics Research Papers
Mathematical Science
Publications

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