Universal point sets for planar three-tree

Abstract

For every $n\in \mathbb{N}$, we present a set $S_n$ of $O(n^{3/2}\log n)$ 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 $S_n$. 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.

revision

References in corpus (1)

• Superpatterns and Universal Point Sets

Cited by in corpus (3)

• Superpatterns and Universal Point Sets
• Drawing Arrangement Graphs In Small Grids, Or How To Play Planarity
• On Universal Point Sets for Planar Graphs