Odd circuits in dense binary matroids

We show that, for each real number α>0 and odd integer k ≥5, there is an integer c such that, if M is a simple binary matroid with | M |≥α2 r( M ) and with no k -element circuit, then M has critical number at most c . The result is an easy application of a regularity lemma for finite abelian grou...

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Bibliographic Details
Published in:Combinatorica (Budapest. 1981) 2017-02, Vol.37 (1), p.41-47
Main Authors: Geelen, Jim, Nelson, Peter
Format: Article
Language:English
Subjects:
Combinatorics
Mathematics
Mathematics and Statistics
Numbers
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Summary:We show that, for each real number α>0 and odd integer k ≥5, there is an integer c such that, if M is a simple binary matroid with | M |≥α2 r( M ) and with no k -element circuit, then M has critical number at most c . The result is an easy application of a regularity lemma for finite abelian groups due to Green.
ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-015-3237-1