  We prove the uniqueness of the infinite connected component for the vacant
set of random interlacements on general vertex-transitive amenable transient
graphs. Our approach is based on connectedness of random interlacements and
differs from the one used by Teixera arXiv:0805.4106 to prove the uniqueness of
the infinite connected component for the vacant set of random interlacements on
$\mathbb Z^d$.
