James Oxley
- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198566946
- eISBN:
- 9780191774904
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566946.003.0011
- Subject:
- Mathematics, Educational Mathematics
This chapter is organized as follows. Section 10.1 presents Gerards' (1989) proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.2 proves the ...
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This chapter is organized as follows. Section 10.1 presents Gerards' (1989) proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.2 proves the ternary-matroid result by modifying the proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.3 focuses on graphic matroids and proves Tutte's (1959) excluded-minor characterization of the class of graphic matroids.Less
This chapter is organized as follows. Section 10.1 presents Gerards' (1989) proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.2 proves the ternary-matroid result by modifying the proof of Tutte's (1958) excluded-minor characterization of the class of regular matroids. Section 10.3 focuses on graphic matroids and proves Tutte's (1959) excluded-minor characterization of the class of graphic matroids.
James Oxley
- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780198566946
- eISBN:
- 9780191774904
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566946.003.0006
- Subject:
- Mathematics, Educational Mathematics
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 ...
More
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.Less
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.
