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

Authors:
M. Chrobak;H. Karloff
Affiliations:
Department of Mathematics, University of California, Riverside, CA;Department of Computer Science, University of Chicago, Chicago, IL
Venue:
ACM SIGACT News
Year:
1989

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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 AC IR2 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 1.098n, for sufficiently large n.