Large Circuits in Binary Matroids of Large Cogirth: I
Hochstättler, Winfried and Jackson, Bill
(1998)
Large Circuits in Binary Matroids of Large Cogirth: I.
Published in:
Journal of Combinatorial Theory B Vol. 74 (1).
pp. 35-52.
Abstract
Let F7 denote the Fano matroid and e be a fixed element of F7. Let P(F7,e) be the family of matroids obtained by taking the parallel connection of one or more copies of F7 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 not have an F7-minor, M is not F * 7 and d >= (r(M)+1)/2 then M has a circuit of size r(M)+1. We also show that if M is connected, e in E(M), M does not have both an F7-minor and an F * 7-minor, and M is not in P(F7,e), then M has a circuit containing e and of size at least d+1.
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Item Type: | Article |
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Citations: | 6 (Google Scholar) | |
Uncontrolled Keywords: | binary matroids hamiltonicity |
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Divisions: | Mathematical Institute |
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ZAIK Number: | zpr97-281 |
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Depositing User: | Winfried Hochstättler |
Date Deposited: | 02 Apr 2001 00:00 |
Last Modified: | 19 Dec 2011 09:46 |
URI: | http://e-archive.informatik.uni-koeln.de/id/eprint/281 |