Rectangular and visibility representations of infinite planar graphs

We provide anew method for extending results on finite planar graphs to the infinite case. Thus a result of Ungar on finite graphs has the following extension: Every infinite, planar, cubic, cyclically 4-edge-connected graph has a representation in the plane such that every edge is a horizontal or vertical straight line segment, and such that no two edges cross. A result of Tamassia and Tollis extends as follows: Every countably infinite planar graph is a subgraph of a visibility graph. Furthermore, every locally finite, 2-connected, planar graph is a visibility graph. (C) 2006 Wiley Periodicals, Inc.