  We consider the canonical contact structures on links of rational surface
singularities with reduced fundamental cycle. These singularities can be
characterized by their dual resolution graphs: the graph is a tree, and the
weight of each vertex is no greater than its negative valency. In a joint work
with Starkston, we previously showed that if the weight of each vertex in the
graph is at most -5, the contact structure has a unique symplectic filling (up
to symplectic deformation and blow-up). The proof was based on a symplectic
analog of de Jong-van Straten's description of smoothings of these
singularities. In this paper, we give a short self-contained proof of
uniqueness of fillings, via analysis of positive monodromy factorizations for
planar open books supporting these contact structures.
