The Common Structure of the Curves Having a Same Gauss Word
Gauss words are finite sequences of letters associated with self-intersecting closed curves in the plane. (These curves have no “triple” self-intersection). These sequences encode the order of intersections on the curves. We characterize, up to homeomorphism, all curves having a given Gauss word. We extend this characterization to the n-tuples of closed curves having a given n-tuple of words, that we call a Gauss multiword. These words encode the self-intersections of the curves and their pairwise intersections. Our characterization uses decompositions of strongly connected graphs in 3-edge-connected components and algebraic terms formalizing these decompositions.
KeywordsDirected Graph Regular Graph Atomic Decomposition Plane Embedding Biconnected Component
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