A unified approach to visibility representations of planar graphs

Abstract

We study visibility representations of graphs, which are constructed by mapping vertices to horizontal segments, and edges to vertical segments that intersect only adjacent vertex-segments. Every graph that admits this representation must be planar. We consider three types of visibility representations, and we give complete characterizations of the classes of graphs that admit them. Furthermore, we present linear time algorithms for testing the existence of and constructing visibility representations of planar graphs. Many applications of our results can be found in VLSI layout. © 1986 Springer-Verlag New York Inc.