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The circuit basis in binary matroids

✍ 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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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

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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

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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