Grid Drawings of 4-Connected Plane Graphs

Grid Drawings of Four-Connected Plane Graphs

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 very simple algorithm to find a grid drawing of any given 4-connected plane graph G with four or more vertices on the outer face. The algorithm take...

Optimal Orthogonal Drawings of Connected Plane Graphs

Minimum-Width Grid Drawings of Plane Graphs

Given a plane graph G, we wish to draw it in the plane in such a way that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in an (n 2) x (n 2) grid (for n ~> 3), and that no grid smal...

Rectangular Grid Drawings of Plane Graphs

The rectangular grid drawing of a plane graph G is a drawing of G such that each vertex is located on a grid point, each edge is drawn as a horizontal or vertical line segment, and the contour of each face is drawn as a rectangle. In this paper we give a simple linear-time algorithm to find a rectangular grid drawing of G if it exists. We also give an upper bound W + H <~ n /2 on the sum of req...

Rectangle-of-Influence Drawings of Four-Connected Plane Graphs

A rectangle-of-in uence drawing of a plane graph G is a straight-line planar drawing of G such that there is no vertex in the proper inside of the axis-parallel rectangle de ned by the two ends of any edge. In this paper, we show that any 4-connected plane graph G with four or more vertices on the outer face has a rectangle-of-in uence drawing in an integer grid such that W + H n, where n is th...