A Universal Point Set for 2-Outerplanar Graphs

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 $O(n\log n)$.