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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 |
Issue 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 |
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: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
Files in This Item:
File | Description | Size | Format | |
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constructions_31.pdf | 269.1 kB | Adobe PDF | View/Open |
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