A proof of McKee's eulerian-bipartite characterization

@article{Woodall1990APO,
  title={A proof of McKee's eulerian-bipartite characterization},
  author={Douglas R. Woodall},
  journal={Discrete Mathematics},
  year={1990},
  volume={84},
  pages={217-220}
}
A proof is given of the result about binary matroids that implies that a connected graph is Eulerian if and only if every edge lies in an odd number of circuits, and a graph is bipartite if and only if every edge lies in an odd number of cocircuits (minimal cutsets). A proof is also given of the result that the edge set of every graph can be expressed as a disjoint union of circuits and cocircuits. No matroid theory is assumed. 

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