Rectangle-Visibility Representations of Bipartite Graphs

The paper considers representations of bipartite graphs as rectangle-visibility graphs, Le., graphs whose vertices are rectangles in the plane, with adjacency detenmned by horizontal and vertical visibility.1t is shown that, for p ~ q, Kp,q has a representation with no rectangles having collinear sides if and only if p ~ 2 or p = 3 and q ~ 4. More generally, it is shown that Kp;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.