2015/12/09 by Jim Geelen, Geelen, Jim, Bert Gerards +3 · 1 citation
Computer Science · #Advanced Graph Theory Research #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.1512.03005
Frame matroids and lifted-graphic matroids are two interesting generalizations of graphic matroids. Here we introduce a new generalization, \em 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 frame matroid.