Diagonal walks on plane graphs and local duality
نویسنده
چکیده
We introduce the notion of local duality for planarmaps, i.e., for graphs embedded in the plane. Local duality is the transitive closure of the relation that transforms a graph that is the union of two connected subgraphs sharing a vertex by dualizing one of the two subgraphs. We prove that two planar maps have the same diagonal walks iff one of them can be transformed into the other by applying symmetry and/or duality and/or local duality. From this result we obtain a characterization of all selfintersecting closed curves in the plane (and even of all finite sets of intersecting closed curves) associated with a given Gauss word (or Gauss multiword). All constructions relative to this result can be formalized in Monadic Second-order logic.
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