On the structure of Schnyder woods on orientable surfaces - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Journal of Computational Geometry Year : 2019

On the structure of Schnyder woods on orientable surfaces

Benjamin Lévêque


We propose a simple generalization of Schnyder woods from the plane to maps on orientable surfaces of higher genus. This is done in the language of angle labelings. Generalizing results of de Fraysseix and Ossona de Mendez, and Felsner, we establish a correspondence between these labelings and orientations and characterize the set of orientations of a map that correspond to such a Schnyder labeling. Furthermore, we study the set of these orientations of a given map and provide a natural partition into distributive lattices depending on the surface homology. This generalizes earlier results of Felsner and Ossona de Mendez. In the particular case of toroidal triangulations, this study enables us to identify a canonical lattice that lies at the core of several bijection proofs.
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Dates and versions

lirmm-02407874 , version 1 (12-12-2019)





Daniel Gonçalves, Kolja Knauer, Benjamin Lévêque. On the structure of Schnyder woods on orientable surfaces. Journal of Computational Geometry, 2019, 10 (1), pp.127-164. ⟨10.20382/jocg.v10i1a5⟩. ⟨lirmm-02407874⟩
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