A note on visibility graphs

Abstract

Given a set S = {s1, s2,..., sn} of vertical line segments, s1, sj see each other if there is a horizontal line segment which intersects them, but does not intersect any other line segment between them. A visibility graph G of vertices {v1, v2,..., vn} is put into a one-to-one correspondence with S, such that si corresponds to v1, and edge {vi, vj} exists in G iff si, sj see each other. We prove that any visibility graph G is ipo-triangular, that is, it can be transformed into a planar multigraph with all triangular finite faces, by successive duplications of existing edges of G. Conversely we prove that any ipo-triangular graph is a visibility graph for some set S. © 1987.