Grid drawings of 4-connected plane graphs

A grid drawing of a plane graph G is a drawing of G on the plane so that al l vertices of G are put on plane grid points and all edges are drawn as str aight Line segments between their endpoints without any edge-intersection. In this paper we give a very simple algorithm to find a grid drawing of any given 4-connected plane graph G with four or more vertices on the outer fa ce. The algorithm takes time O(n) and yields a drawing in a rectangular gri d of width [n/2] - 1 and height [n/2] if G has n vertices. The algorithm is best possible in the sense that there are an infinite number of 4-connecte d plane graphs, any grid drawings of which need rectangular,grids of width [n/2] - 1 and height [n/2].