It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed cdn, where c is a constant. This bound, conjectured by Brass, cannot be improved, apart from the value of the constant. We strengthen and generalize this result to the case when the graph has a crossing-free drawing on an orientable surface of higher genus and there is no restriction on the degrees of the vertices. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Fach, J., & Tóth, G. (2006). Crossing number of toroidal graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3843 LNCS, pp. 334–342). https://doi.org/10.1007/3-540-33700-8_28
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