A Universal Point Set for 2-Outerplanar Graphs

Abstract

A point set $$S \subseteq \mathbb {R}^2$$ is universal for a class $$\mathcal G$$ if every graph of $$\mathcal{G}$$ has a planar straight-line embedding on S. It is well-known that the integer grid is a quadratic-size universal point set for planar graphs, while the existence of a sub-quadratic universal point set for them is one of the most fascinating open problems in Graph Drawing. Motivated by the fact that outerplanarity is a key property for the existence of small universal point sets, we study 2-outerplanar graphs and provide for them a universal point set of size $$On \log n$$.