A 1.235 lower bound on the number of points needed to draw all n-vertex planar graphs

Abstract

We study a problem of lower bounds on straight line drawings of planar graphs. We show that at least 1.235· n points in the plane are required to draw each n-vertex planar graph with edges drawn as straight line segments (for sufficiently large n). This improves the previous best bound of 1.206· n (for sufficiently large n) due to Chrobak and Karloff [Sigact News 20 (4) (1989) 83–86]. Our contribution is twofold: we improve the lower bound itself and we give a significantly simpler and more straightforward proof.