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arXiv · 1507.05461

Encoding toroidal triangulations

Vincent Despré·Daniel Gonçalves·Benjamin Lévêque
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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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Vincent Despré, Daniel Gonçalves, Benjamin Lévêque. 2015-07-20. Encoding toroidal triangulations. https://arxiv.org/abs/1507.05461

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