# Diagonal walks on plane graphs and local duality

@inproceedings{LaBRI2006DiagonalWO, title={Diagonal walks on plane graphs and local duality}, author={Bruno Courcelle LaBRI}, year={2006} }

- Published 2006

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… CONTINUE READING

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