Nakajima's quiver varieties and triangular bases of bipartite cluster algebras

Berenstein and Zelevinsky introduced quantum cluster algebras {BZ1} and the triangular bases {BZ2}. The support conjecture proposed in {LLRZ}, which asserts that the support of each triangular basis element for a rank-2 cluster algebra is bounded by an explicitly described region, was established in {L} for skew-symmetric rank-2 cluster algebras. In this paper we extend this result by proving a bound on the support of each triangular basis element for bipartite cluster algebras.