On rectangle visibility graphs

Abstract

We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical lines-of-sight. Such a drawing is useful, for example, when the vertices of the graph contain information that we wish displayed on the drawing; it is natural to write this information inside the rectangle corresponding to the vertex. We call a graph that can be drawn in this fashion a rectangle-visibility graph, or RVG. Our goal is to find classes of graphs that are RVGs. We obtain several results: 1. For 1 ≤ k ≤ 4, k-trees are RVGs. 2. Any graph that can be decomposed into two caterpillar forests is an RVG. 3. Any graph whose vertices of degree four or more form a distance-two independent set is an RVG. 4. Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.