TESSELLATION AND VISIBILITY REPRESENTATIONS OF MAPS ON THE TORUS

Authors
MOHAR B ROSENSTIEHL P
Citation
B. Mohar et P. Rosenstiehl, TESSELLATION AND VISIBILITY REPRESENTATIONS OF MAPS ON THE TORUS, Discrete & computational geometry, 19(2), 1998, pp. 249-263
Citations number
15
Categorie Soggetti
Computer Science Theory & Methods",Mathematics,"Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
19
Issue
2
Year of publication
1998
Pages
249 - 263
Database
ISI
SICI code
0179-5376(1998)19:2<249:TAVROM>2.0.ZU;2-V
Abstract
The model of the torus as a parallelogram in the plane with opposite s ides identified enables us to define two families of parallel lines an d to tessellate the torus, then to associate to each tessellation a to roidal map with an upward drawing. It is proved that a toroidal map ha s a tessellation representation if and only if its universal cover is 2-connected. Those graphs that admit such an embedding in the torus ar e characterized.