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Article Dans Une Revue Discrete and Computational Geometry Année : 2017

Encoding toroidal triangulations

Résumé

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).

Dates et versions

hal-01488931 , version 1 (14-03-2017)

Identifiants

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