  We show that the arc graph of $S_g^1$ is a coarse Lipschitz retract of the
free splitting complex of $F_{2g}$. We also show that the arc and curve graph
of $S_g^1$ is a coarse Lipschitz retract of both the cyclic splitting graph of
$F_{2g}$ and the maximally cyclic splitting graph of $F_{2g}$.
