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Matroid Theory$
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Matroid Theory

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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Graphic Matroids

Graphic Matroids

Chapter:
(p.135) 5 Graphic Matroids
Source:
Matroid Theory
Author(s):

James Oxley

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198566946.003.0006

This chapter examines graphic matroids in more detail. In particular, it presents several proofs delayed from Chapters 1 and 2, including proofs that a graphic matroid is representable over every field, and that a cographic matroid M*(G) is graphic only if G is planar. The main result of the chapter is Whitney's 2-Isomorphism Theorem, which establishes necessary and sufficient conditions for two graphs to have isomorphic cycle matroids.

Keywords:   graphic matroid, cographic matroid, 2-Isomorphism Theorem, isomorphic cycle matroids

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