Tessellation and Visibility Representations of Maps on the Torus

The model of the torus as a parallelogram in the plane with opposite sides identified enables us to define two families of parallel lines and to tessellate the torus, then to associate to each tessellation a toroidal map with an upward drawing. It is proved that a toroidal map has a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embedding in the torus are characterized.

Authors and Affiliations

1. Department of Mathematics, University of Ljubljana, Slovenia , , , , , , SI

   B. Mohar

2. Centre d'Analyse et de Mathématique Sociales, EHESS, Paris, France , , , , , , FR

   P. Rosenstiehl

Received November 22, 1995, and in revised form May 1, 1997.

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