Inner Rectangular Drawings of Plane Graphs

Abstract

A drawing of a plane graph is called an inner rectangular drawing if every edge is drawn as a horizontal or vertical line segment so that every inner face is a rectangle In this paper we show that a plane graph G has an inner rectangular drawing D if and only if a new bipartite graph constructed from G has a perfect matching We also show that D can be found in time O(n1.5/log n) if G has n vertices and a sketch of the outer face is prescribed, that is, all the convex outer vertices and concave ones are prescribed.