Abstract
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|≥α2r(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.
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This research was partially supported by a grant from the Office of Naval Research [N00014-10-1-0851].
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Geelen, J., Nelson, P. Odd circuits in dense binary matroids. Combinatorica 37, 41–47 (2017). https://doi.org/10.1007/s00493-015-3237-1
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DOI: https://doi.org/10.1007/s00493-015-3237-1