Abstract
In this paper we study 3-dimensional visibility representations of complete graphs. The vertices are represented by equal regular polygons lying in planes parallel to the xy-plane. Two vertices are adjacent if and only if the two corresponding polygons see each other-i.e. it is possible to construct an abscissa perpendicular to the xy-plane connecting the two polygons and avoiding all the others. We give the bounds for the maximal size f(k) of a clique represented by regular k-gons: (equation-found) 22k and we present a particular result for triangles: f(3) ≥ 14.
Cite
CITATION STYLE
Babilon, R., Nyklová, H., Pangrác, O., & Vondrák, J. (1999). Visibility representations of complete graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1731, pp. 333–341). Springer Verlag. https://doi.org/10.1007/3-540-46648-7_34
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