Rectangle-visibility representations of bipartite graphs

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...

On Rectangle Visibility Graphs

In this paper we consider the problem of drawing a graph in the plane so that the vertices of the graph are drawn as rectangles and the edges are horizontal or vertical line segments. We are in particular interested in drawings where each of the line segments can be thickened to have positive width, and none of these thickened segments (which we call bands of visibility) intersects the interior...

Rectangle and Box Visibility Graphs in 3D

We discuss rectangle and box visibility representations of graphs in 3-dimensional space. In these representations, vertices are represented by axis-aligned disjoint rectangles or boxes. Two vertices are adjacent if and only if their corresponding boxes see each other along a small axis-parallel cylinder. We concentrate on lower and upper bounds for the size of the largest complete graph that c...

Directed rectangle visibility graphs have unbounded dimension

On Rectangle Visibility Graphs. III. External Visibility and Complexity