Abstract. Graph pattern matching is a central application in many fields. In various areas, the structure of the pattern can only be approximated and exact matching is then too accurate. We focus here on approximations declared by the user within the pattern (optional nodes and forbidden arcs), covering graph/subgraph mono/isomorphism problems. In this paper, we show how the integration of two domains of computation over countable structures, graphs and maps, can be used for modeling and solving various graph matching problems from the simple graph isomorphism to approximate graph matching. To achieve this, we extend map variables allowing the domain and range to be non-fixed and constrained. We describe how such extended maps are designed then realized on top of finite domain and finite set variables with specific propagators. We show how a single monomorphism constraint is sufficient to model and solve those multiples graph matching problems. Furthermore, our experimental results show that our CP approach is competitive with a state of the art algorithm for subgraph isomorphism.