Chatterjee et al. have recently shown the utility of SAT in solving a class of planning problems with partial observability. A core component of their logical formulation of planning is constraints expressing s-t-reachability in directed graphs. In this work, we show that the scalability of the approach can be dramatically improved by using dedicated graph constraints, and that a far broader class of important planning problems can be expressed in terms of s-t-reachability and acyclicity constraints.