, Volume 37, Issue 1, pp 41–47 | Cite as

Odd circuits in dense binary matroids

  • Jim Geelen
  • Peter Nelson
Original Paper


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.

Mathematics Subject Classification (2000)



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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada

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