Rectangle-visibility representations of bipartite graphs

Abstract

The paper considers representations of bipartite graphs as rectanglevisibility graphs, i.e., graphs whose vertices are rectangles in the plane, with adjacency determined by horizontal and vertical visibility. It is shown that, for p≤q, K _{p, q} has a representation with no rectangles having collinear sides if and only if p≤3 or p=3 and q≤4. More generally, it is shown that K _{p, q} is a rectangle-visibility graph if and only if p≤4. Finally, it is shown that every bipartite rectangle-visibility graph on n≥4 vertices has at most 4n−12 edges.

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