Quasi‐graphic matroids *

@article{Geelen2018QuasigraphicM,
  title={Quasi‐graphic matroids *},
  author={James F. Geelen and Bert Gerards and Geoff Whittle},
  journal={Journal of Graph Theory},
  year={2018},
  volume={87},
  pages={253 - 264}
}
Frame 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 3‐connected matroid is quasi‐graphic. The main result is that every 3‐connected representable quasi‐graphic matroid is either a lifted‐graphic matroid or a frame matroid. 

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