The Imbedding Theorem : Every compact metrizable space $X$ of topological dimension $m$ can be imbedded in $\Bbb R^{2m+1}$
Following above thoerem, I could roughly guess for given a finite graph $G(V,E)$ if G is compact metrizable space, I could guess the $2m+1$ which is sufficient to embed the graph itself.
Is $G$ Compact? Is $G$ metrizable? Either one of two questions are not obvious to anwer to me.
If so, how could one find topological dimension $m$ of $G$?