Representation of Graphs on a Torus
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Representation of Graphs on a Torus F.J. Cobos, J.C. Dana, A. Márquez and F. Mateos Dpto. de Matemática Aplicada I. Facultad de Informática y Estadı́stica. Universidad de Sevilla. Avda. Reina Mercedes s/n. 41012-Sevilla (Spain) Abstract A complete characterization of the class of graphs that admit a toroidal visibility representation is given. In that representation, vertices map to arcs of parallels in the torus and two vertices are joined by an edge if their corresponded intervals are joined by a strip parallel to the meridians in the torus. Moreover, linear time algorithms are given for testing the existence and constructing such a representation. We also study the relation of these graphs with those admitting a planar visibility representation and those with a cylindrical visibility representation.
