Quaternary matroids are vf-safe

Abstract

Binary delta-matroids are closed under vertex flips, which consist of the natural operations of twist and loop complementation. In this note we provide an extension of this result from GF(2) to GF(4). As a consequence, quaternary matroids are "safe" under vertex flips (vf-safe for short). As an application, we find that the matroid of a bicycle space of a quaternary matroid is independent of the chosen representation. This extends a result of Vertigan [J. Comb. Theory B (1998)] concerning the bicycle dimension of quaternary matroids.