Abstract

This paper considers a 3-dimensional visibility representation of cliques Kn. In this representation, the objects representing the vertices are 2-dimensional and lie parallel to the x, y-plane, and two vertices of the graph are adjacent if and only if their corresponding objects see each other by a line of sight parallel to the z-axis that intersects the interiors of the objects. In particular, we represent vertices by unit discs and by discs of arbitrary radii (possibly different for different vertices); we also represent vertices by axis-aligned unit squares, by axis-aligned squares of arbitrary size (possibly different for different vertices), and by axis-aligned rectangles.

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