On characterizations of binary and graphic matroids
β Scribed by Jean-Paul Doignon
- Book ID
- 107748380
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 218 KB
- Volume
- 37
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
In this paper we present the characterization of graphic matroids using the concept of a chord. Then we apply this characterization to solve a problem of Szamkolowicz [9]. One of the deepest theorems in the theory of matroids is Tuttes excludedminor characterization of graphic matroids [ 111. The p
## Abstract In this paper we present a relatively simple proof of Tutt's characterization of graphic matroids. The proof uses the notion of βsigned graphβ and it is βgraphicβ in the sense that it can be presented almost entirely by drawing (signed) graphs. Β© 1995 John Wiley & Sons, Inc.
1+ Introductim ## 2. &tnatrsids An Z-nt~rfpis is 8 @-I matrix having thk. I+ 7 .Fyaty tha? some permuta-tion of its distinct ~ofutnns is the matrix J: I,\* fair some intttgcr r 2 '1. JP is the r \* r matrix of all 1's and lr is thbz F X r identity. Given an [-maitrix with r rows. the follc:wing pr
## Abstract A wellβknown result of Tutte states that a 3βconnected graph __G__ is planar if and only if every edge of __G__ is contained in exactly two induced nonβseparating circuits. Bixby and Cunningham generalized Tutte's result to binary matroids. We generalize both of these results and give n