  We show that for a sufficiently simple surface $S$, a right-angled Artin
group $A(\Gamma)$ embeds into $\Mod(S)$ if and only if $\Gamma$ embeds into the
curve graph $\mC(S)$ as an induced subgraph. When $S$ is sufficiently
complicated, there exists an embedding $A(\Gamma)\to\Mod(S)$ for some $\Gamma$
not contained in $\mC(S)$.
