Knowledge graphs such as Yago and Freebase have become a powerful asset for enhancing search, and are being intensively used in both academia in industry. Many existing knowledge graphs are either available as Linked Open Data, or they can be exported as RDF datasets enhanced with background knowledge in the form of an OWL 2 ontology. Faceted search is the de facto approach for exploratory search in many online applications, and has been recently proposed as a suitable paradigm for querying RDF repositories. In this paper, we provide rigorous theoretical underpinnings for faceted search in the context of RDFbased knowledge graphs enhanced with OWL 2 ontologies. We identify well-defined fragments of SPARQL that can be naturally captured using faceted search as a query paradigm, and establish the computational complexity of answering such queries. We also study the problem of updating faceted interfaces, which is critical for guiding users in the formulation of meaningful queries during exploratory search. We have implemented our approach in a fully-fledged faceted search system, SemFacet, which we have evaluated over the Yago knowledge graph.