Skip to Main content Skip to Navigation
Journal articles

On the structure of Schnyder woods on orientable surfaces

Daniel Gonçalves 1 Kolja Knauer 2 Benjamin Lévêque 3 
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
3 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : 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.
Document type :
Journal articles
Complete list of metadata

Cited literature [28 references]  Display  Hide  Download
Contributor : Daniel Gonçalves Connect in order to contact the contributor
Submitted on : Thursday, December 12, 2019 - 4:41:26 PM
Last modification on : Friday, August 5, 2022 - 3:02:53 PM
Long-term archiving on: : Friday, March 13, 2020 - 11:22:02 PM


Distributed under a Creative Commons Attribution 4.0 International License



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



Record views


Files downloads