Grid Drawings of Five-Connected Plane Graphs

Abstract

A grid drawing of a plane graph G is a drawing of G on the plane so that all vertices of G are put on plane grid points and all edges are drawn as straight line segments between their endpoints without any edge-intersection. In this paper we give a linear-time algorithm to find a grid drawing of any given 5-connected plane graph G with five or more vertices on the outer face. The size of the drawing satisfies W + H ≤ n−2, where n is the number of vertices in G, W is the width and H is the height of the grid drawing.