Problem. Given a tree do we need fewer lines in 3D than in 2D in order to draw it straightline and crossing-free?
(Asked 01.10.2016 by Alexander Wolff on page 20 of Volume 1 of the Lviv Scottish Book).
Clarification. For a given finite simple graph $G$ by $\rho^1_2(G)$ (resp. $\rho^1_3(G)$) we denote the minimal number of straight lines needed to cover all edges in a straight-line crossing-free drawing of the graph $G$ in 2D (resp. 3D). We are asking for a tree $T$ such that $\rho^1_3(T)<\rho^1_2(T)$.
The problem was originally asked 11.06.2016 by Oleg Verbitsky.