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 matroid is quasi-graphic. The main result of the article is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a frame matroid.

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Journal of Graph Theory
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Geelen, J, Gerards, A.M.H, & Whittle, G. (2018). Quasi-Graphic Matroids (retracted). Journal of Graph Theory, 87(2), 265–265. doi:10.1002/jgt.22143