3D Visibility Representations of Complete Graphs

This paper continues the study of 3D visibility representations of complete graphs where vertices are represented by equal convex polygons lying in planes parallel to the xy-plane. Edges correspond to the z-parallel visibility among these polygons.We give several bounds on the size of the largest complete graph that has a 3D visibility representation with particular properties. Namely we improve the best known lower bound for representations by regular n-gons from $\lfloor \frac{n+1}{2}\rfloor+2$ to n+1 and the upper bound from $2^{2^{n}}$ to $\left({6n-3 \atop 3n-1}\right)-3$.