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

Uniqueness of the infinite connected component for the vacant set of random interlacements on amenable transient graphs