The circuit basis in binary matroids
β Scribed by Judith Q Longyear
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 340 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
Hartvigsen and Zemel have obtained a characterization of those graphs which have every circuit basis fundamental. We consider the corresponding problem for binary matroids. We show that, in general, the class of binary matroids for which every circuit basis is fundamental is not closed under the tak
Let F 7 denote the Fano matroid and e be a fixed element of F 7 . Let P(F 7 , e) be the family of matroids obtained by taking the parallel connection of one or more copies of F 7 about e. Let M be a simple binary matroid such that every cocircuit of M has size at least d 3. We show that if M does no
Let F 7 denote the Fano matroid and M be a simple connected binary matroid such that every cocircuit of M has size at least d 3. We show that if M does not have an F 7 -minor, M{F\* 7 , and d Γ [5, 6, 7, 8], then M has a circuit of size at least min[r(M )+1, 2d ]. We conjecture that the latter resul