On excluded minors for classes of graphical matroids

摘要

Frame matroids and lifted-graphic matroids are two distinct minor-closed classes of matroids, each of which generalises the class of graphic matroids. The class of quasi-graphic matroids, recently introduced by Geelen, Gerards, and Whittle, simultaneously generalises both the classes of frame and lifted-graphic matroids. Let m be one of these three classes, and let r be a positive integer. We show that M has only a finite number of excluded minors of rank r. (C) 2018 Elsevier B.V. All rights reserved.