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A 1.235 lower bound on the number of points needed to draw all n-vertex planar graphs
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Computational Geometry: Theory and Applications
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For every n∈ℕ, we present a set Sn of O(n5/3) points in the plane such that every planar 3-tree with n vertices has a straight-line embedding in the plane in which the vertices are mapped to a subset of Sn. This is the first subquadratic upper bound on the size of universal point sets for planar 3-trees, as well as for the class of 2-trees and serial parallel graphs.