The 9-connected Excluded Minors for the Class of Quasi-graphic Matroids

2021/06/18 by Rong Chen, Chen, Rong
Engineering · #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2106.09955

Abstract

The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, is minor closed and contains both the class of lifted-graphic matroids and the class of frame matroids, each of which generalises the class of graphic matroids. In this paper, we prove that the matroids U_3,7 and U_4,7 are the only 9-connected excluded minors for the class of quasi-graphic matroids.

Related

• On excluded minors for classes of graphical matroids
• On excluded minors of connectivity 2 for the class of frame matroids
• The excluded minors for the class of matroids that are graphic or bicircular lift
• The excluded minors for near-regular matroids
• The Highly Connected Matroids in Minor-closed Classes