Rectangle-Visibility Representations of Bipartite Graphs (Extended Abstract)

The paper considers representations of bipartite graphs as rectangle-visibility 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 \leq p, K_{p,q} has a representation with no rectangles having collinear sides if and only if p < 3 or p = 3 and q \leq 4. More generally, it is shown that K_{p,q} is a rectangle-visibility graph if and only if p \leq 4. Finally, it is shown that every bipartite rectangle-visibility graph on n \geq 4 vertices has at most 4n - 12 edges