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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/7066

Title: Constructing internally 4-connected binary matroids
Authors: Chun, C
Mayhew, D
Oxley, J
Keywords: Chain theorem
Inductive construction
Internally 4-connected
Binary matroid
Publication Date: 2013
Publisher: Elsevier
Citation: Advances in Applied Mathematics, 50(1): 16 - 45, Jan 2013
Abstract: In an earlier paper, we proved that an internally 4-connected binary matroid with at least seven elements contains an internally 4-connected proper minor that is at most six elements smaller. We refine this result, by giving detailed descriptions of the operations required to produce the internally 4-connected minor. Each of these operations is top-down, in that it produces a smaller minor from the original. We also describe each as a bottom-up operation, constructing a larger matroid from the original, and we give necessary and su fficient conditions for each of these bottom-up moves to produce an internally 4-connected binary matroid. From this, we derive a constructive method for generating all internally 4-connected binary matroids.
Description: This is the post-print version of the Article - Copyright @ 2013 Elsevier
Sponsorship: This study is supported by NSF IRFP Grant 0967050, the Marsden Fund, and the National Security Agency.
URI: http://www.sciencedirect.com/science/article/pii/S0196885812000930
http://bura.brunel.ac.uk/handle/2438/7066
DOI: http://dx.doi.org/10.1016/j.aam.2012.03.005
ISSN: 0196-8858
Appears in Collections:School of Information Systems, Computing and Mathematics Research Papers
Mathematical Science
Publications

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