Vf-safe delta-matroids have the desirable property of behaving well under certain duality operations. Several important classes of delta-matroids are known to be vf-safe, including the class of ribbon-graphic delta-matroids, which is related to the class of ribbon graphs or embedded graphs in the same way that graphic matroids correspond to graphs. In this paper, we characterize vf-safe delta-matroids and ribbon-graphic delta-matroids by finding the minimal obstructions, called 3-minors, to belonging to the class. We find the unique (up to twisted duality) excluded 3-minor within the class of set systems for the class of vf-safe delta-matroids. In "Circle graph obstructions under pivoting", Geelen and Oum found the 166 (up to twists) excluded minors for ribbon-graphic delta-matroids. By translating Bouchet's characterization of circle graphs to the language of 3-minors, we show that this class can also be characterized amongst delta-matroids by a set of three excluded 3-minors up to tw 查看全文>>