On recognising frame and lifted-graphic matroids

Abstract

We prove that there is no polynomial $p(\cdot)$ with the property that a matroid $M$ can be determined to be either a lifted-graphic or frame matroid using at most $p(|M|)$ rank evaluations. This resolves two conjectures of Geelen, Gerards and Whittle (Quasi-graphic matroids, arXiv:1512.03005v1).