Toroidal maps : Schnyder woods, orthogonal surfaces and straight-line representations

Details Toroidal maps : Schnyder woods, orthogonal surfaces and straight-line representations Toroidal maps : Schnyder woods, orthogonal surfaces and straight-line representations

2012-02-04

arxiv.org/abs/1202.0911v1

Computer Science

Discrete Mathematics

Scientific paper

A Schnyder wood is an orientation and coloring of the edges of a planar map satisfying a simple local property. We propose a generalization of Schnyder woods to toroidal maps with application to graph drawing. We prove the existence of these Schnyder woods for toroidal triangulations. We show that Schnyder woods can be used to embed the universal cover of a toroidal map on an infinite and periodic orthogonal surface. Finally we use this embedding to obtain a straight-line flat torus representation of any toroidal map in a polynomial size grid.

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