Large Circuits in Binary Matroids of Large Cogirth: I
HochstÃ¤ttler, 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. 3552.
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 F7minor, 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 F7minor and an F * 7minor, 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 

Citations:  6 (Google Scholar)  
Uncontrolled Keywords:  binary matroids hamiltonicity 
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Divisions:  Mathematical Institute 
Related URLs: 
ZAIK Number:  zpr97281 

Depositing User:  Winfried HochstÃ¤ttler 
Date Deposited:  02 Apr 2001 00:00 
Last Modified:  19 Dec 2011 09:46 
URI:  http://earchive.informatik.unikoeln.de/id/eprint/281 