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The Common Structure of the Curves Having a Same Gauss Word

  • Bruno CourcelleEmail author
Chapter
Part of the Emergence, Complexity and Computation book series (ECC, volume 12)

Abstract

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.

Keywords

Directed Graph Regular Graph Atomic Decomposition Plane Embedding Biconnected Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LaBRIBordeaux University and CNRSBordeauxFrance

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