universal set

Universal point sets for planar graphs ★★★

Author(s): Mohar

We say that a set $ P \subseteq {\mathbb R}^2 $ is $ n $-universal if every $ n $ vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in $ P $, and all edges are (non-intersecting) straight line segments.

Question   Does there exist an $ n $-universal set of size $ O(n) $?

Keywords: geometric graph; planar graph; universal set

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