Quasi-graphic matroids

@article{Geelen2018QuasigraphicM,
  title={Quasi-graphic matroids},
  author={James F. Geelen and Bert Gerards and Geoff Whittle},
  journal={J. Graph Theory},
  year={2018},
  volume={87},
  pages={253-264}
}
htmlabstractFrame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, quasi-graphic matroids, that unifies these two existing classes. Unlike frame matroids and lifted-graphic matroids, it is easy to certify that a matroid is quasi-graphic. The main result of the paper is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a rame matroid. 

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