A lower bound on the size of universal sets for planar graphs

Abstract

A Fáry embedding of a planar graph G is an embedding of G into the plane, no edges crossing, with each edge embedded as a straight line segment. A set A C IR 2 is said to be n-universal if every n -node planar graph has a Fáry embedding into A. We show that any n -universal set has size at least 1.098 n , for sufficiently large n.