2 problems

Let $G$ be a graph on $n$ vertices. Its separation dimension is the smallest integer $d$ for which there is an embedding $\phi:G\rightarrow\mathbb{R}^{d}$ such that, for every pair…

Let $G$ be a graph. Its separation dimension is the smallest positive integer $d$ for which there is an embedding $\phi:V(G)\to\mathbb{R}^d$ such that, whenever $\\{x,y\\}$ and…