Abstract
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.
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