Constructing internally 4-connected binary matroids

Autor: Dillon Mayhew, Carolyn Chun, James Oxley
Rok vydání: 2013
Předmět:
Zdroj: Advances in Applied Mathematics. 50(1):16-45
ISSN: 0196-8858
DOI: 10.1016/j.aam.2012.03.005
Popis: This is the post-print version of the Article - Copyright @ 2013 Elsevier 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. This study is supported by NSF IRFP Grant 0967050, the Marsden Fund, and the National Security Agency.
Databáze: OpenAIRE