Continuous Graph Pattern Matching (GPM) is an extended version of the traditional GPM that is evaluated over Knowledge Graph (KG) streams. It comes with additional constraints of scalability and near-to-real-time response, and is used in many applications such as real-time knowledge management, social networks and sensor networks. Hence, existing GPM solutions for static KGs are not directly applicable in this setting. This paper studies continuous GPM over KG streams for two different executional models: event-based and incremental. We first propose a query-based graph pruning technique to filter the unnecessary triples from a KG event. The pruned events are materialized in a set of vertically partitioned tables. We then use a hybrid join-and-explore technique to further prune and finally match the triples within a KG event. Considering the on-the-fly execution of queries over pruned KG events, we use an automata-based model to guide the join and exploration process. This leads to an index-free solution optimised for streaming environments. Experimental results with both synthetic and real-world datasets confirm that our system outperforms the state-of-the-art solutions by (on average) one to two orders of magnitude; in terms of performance and scalability.