This paper proposes a 3-dimensional visibility representation of graphs G = (V, E) in which vertices are mapped to rectangles floating in R 3 parallel to the x, y-plane, with edges represented by vertical lines of sight. We apply an extension of the Erdős-Szekeres Theorem in a geometric setting to obtain an upper bound of n = 56 for the largest representable complete graph Kn. On the other hand, we show by construction that n ≥ 22. These are the best existing bounds. We also note that planar

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... phs and complete bipartite graphs Km,n are representable, but that the family of representable graphs is not closed under graph minors.