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Encoding toroidal triangulations

Vincent Despré 1, 2 Daniel Gonçalves 3 Benjamin Lévêque 2
2 G-SCOP_OC - Optimisation Combinatoire
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
3 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Poulalhon and Schaeffer introduced an elegant method to linearly encode a planar triangulation optimally. The method is based on performing a special depth-first search algorithm on a particular orientation of the triangulation: the minimal Schnyder wood. Recent progress toward generalizing Schnyder woods to higher genus enables us to generalize this method to the toroidal case. In the plane, the method leads to a bijection between planar triangulations and some particular trees. For the torus we obtain a similar bijection but with particular unicellular maps (maps with only one face).
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https://hal.archives-ouvertes.fr/hal-01488931
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Submitted on : Tuesday, March 14, 2017 - 9:39:47 AM
Last modification on : Friday, January 7, 2022 - 3:53:19 AM

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Vincent Despré, Daniel Gonçalves, Benjamin Lévêque. Encoding toroidal triangulations. Discrete and Computational Geometry, Springer Verlag, 2017, 57 (3), pp.507-544. ⟨10.1007/s00454-016-9832-0⟩. ⟨hal-01488931⟩

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