  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).

Discrete Mathematics;Computational Geometry;Combinatorics