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 paper is that every 3-connected representable quasi-graphic matroid is either a lifted-graphic matroid or a rame matroid.
|matroids, representation, graphic matroids, frame matroids.|
|Matroids, geometric lattices (msc 05B35)|
|Logistics (theme 3)|
|Organisation||Networks and Optimization|
Geelen, J, Gerards, A.M.H, & Whittle, G. (2015). Quasi-graphic matroids.