Testing model transformations requires input models which are graphs of inter-connected objects that must conform to a meta-model and meta-constraints from heterogeneous sources such as well-formedness rules, transformation pre-conditions, and test strategies. Manually specifying such models is tedious since models must simultaneously conform to several meta-constraints. We propose automatic model generation via constraint satisfaction using our tool Cartier for model transformation testing. Due to the virtually infinite number of models in the input domain we compare strategies based on input domain partitioning to guide model generation. We qualify the effectiveness of these strategies by performing mutation analysis on the transformation using generated sets of models. The test sets obtained using partitioning strategies gives mutation scores of up to 87\% vs. 72\% in the case of unguided/random generation. These scores are based on analysis of 360 automatically generated test models for the representative transformation of UML class diagram models to RDBMS models.