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

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

Geelen, J., Gerards, B., & Whittle, G. (2018). Quasi-graphic matroids (corrected version of a paper that was previously retracted at the request of the authors). Journal of Graph Theory, 87(2), 253–264. doi:10.1002/jgt.22177