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Matroid Theory$
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James Oxley

Print publication date: 2011

Print ISBN-13: 9780198566946

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780198566946.001.0001

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Seymour's Decomposition Theorem

Seymour's Decomposition Theorem

Chapter:
(p.489) 13 Seymour's Decomposition Theorem
Source:
Matroid Theory
Author(s):

James Oxley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566946.003.0014

The excluded-minor theorem provides one characterization of the class of regular matroids. This chapter presents a different characterization of this class: a decomposition theorem for members of the class, which was proved by Seymour. This theorem has a number of important consequences, one of which is that it leads to a polynomial-time algorithm to test whether a given real matrix is totally unimodular.

Keywords:   regular matroids, excluded-minor theorem, decomposition theorem, polynomial-time algorithm, real matrix, unimodular

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