On the structure of Schnyder woods on orientable surfaces

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 orien...

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Bibliographic Details
Published inJournal of computational geometry Vol. 10; no. 1; pp. 127 - 164
Main Authors Gonçalves, Daniel, Knauer, Kolja, Lévêque, Benjamin
Format Journal Article
LanguageEnglish
Published Carleton University, Computational Geometry Laboratory 2019
Subjects
Computer Science
Discrete Mathematics
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Summary: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.
ISSN:1920-180X
1920-180X
DOI:10.20382/jocg.v10i1a5