Pattern matching is a fundamental tool for answering complex graph queries. Unfortunately, existing solutions have limited capabilities: they do not scale to process large graphs and/or support only a restricted set of search templates or usage scenarios. We present an algorithmic pipeline that bases pattern matching on constraint checking. The key intuition is that each vertex or edge participating in a match has to meet a set of constrains implicitly specified by the search template. The pipeline we propose, generates these constraints and iterates over them to eliminate all the vertices and edges that do not participate in any match, and reduces the background graph to a subgraph which is the union of all matches. Additional analysis can be performed on this annotated, reduced graph, such as full match enumeration. Furthermore, a vertex-centric formulation for constraint checking algorithms exists, and this makes it possible to harness existing high-performance, vertex-centric graph processing frameworks. The key contribution of this work is a design following the constraint checking approach for exact matching and its experimental evaluation. We show that the proposed technique: (i) enables highly scalable pattern matching in labeled graphs, (ii) supports arbitrary patterns with 100% precision, (iii) always selects all vertices and edges that participate in matches, thus offering 100% recall, and (iv) supports a set of popular data analysis scenarios. We implement our approach on top of HavoqGT, an open-source asynchronous graph processing framework, and demonstrate its advantages through strong and weak scaling experiments on massive scale real-world (up to 257 billion edges) and synthetic (up to 4.4 trillion edges) labeled graphs respectively, and at scales (1,024 nodes / 36,864 cores), orders of magnitude larger than used in the past for similar problems.