Visibility Representations of Complete Graphs

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: k+1 2 + 2 ≤ f(k) ≤ 22k and we present a particular result for triangles: f(3) ≥ 14.

• Type: Conference
• Year: 1999
• Where: GD
• Authors: Robert Babilon, Helena Nyklová, Ondrej Pangrác, Jan Vondrák
• Keywords: 3-dimensional Visibility Representations, Computer Graphics, Corresponding Polygons, Equal Regular Polygons, GD 1999