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Large Circuits in Binary Matroids of Large Cogirth, II

✍ Scribed by Winfried Hochstättler; Bill Jackson


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
223 KB
Volume
74
Category
Article
ISSN
0095-8956

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✦ Synopsis


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  [5, 6, 7, 8], then M has a circuit of size at least min[r(M )+1, 2d ]. We conjecture that the latter result holds for all d 3. 1998 Academic Press (b) Suppose M is connected, e # E(M ), and every cocircuit Y of M with e  Y has size at least d. If M  P(F 7 , e) then M has a circuit C containing e and of size at least d+1.


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