Solution (source code)

= Solution

For a finite <graph> $\Gamma$, its <Right-angled Artin group> is
$$
A_\Gamma=\left\langle v\in V(\Gamma)\mathrel{\middle|}[v,w]=1\text{ for every }\{v,w\}\in E(\Gamma)\right\rangle.
$$
Its <Salvetti complex> $S_\Gamma$ is the one-vertex <cube complex> with an oriented loop labelled $v$ for each vertex of $\Gamma$, a square torus for every edge, and more generally one cubulated $k$-torus for every $k$-clique, attached compatibly along coordinate subtori. Thus $\pi_1(S_\Gamma)\cong A_\Gamma$. The <vertex link of a Salvetti complex> is flag, so $S_\Gamma$ is a <nonpositively curved cube complex>.