Quasi-graphic matroids (corrected version of a paper that was previously retracted at the request of the authors)

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. Copyright

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