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The excluded 3-minors for vf-safe delta-matroids. (arXiv:1807.01376v1 [math.CO])
来源于:arXiv
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
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