Short texts challenge NLP tasks such as named entity recognition, disambiguation, linking and relation inference because they do not provide sufficient context or are partially malformed (e.g. wrt. capitalization, long tail entities, implicit relations). In this work, we present the Falcon approach which effectively maps entities and relations within a short text to its mentions of a background knowledge graph. Falcon overcomes the challenges of short text using a light-weight linguistic approach relying on a background knowledge graph. Falcon performs joint entity and relation linking of a short text by leveraging several fundamental principles of English morphology (e.g. compounding, headword identification) and utilizes an extended knowledge graph created by merging entities and relations from various knowledge sources. It uses the context of entities for finding relations and does not require training data. Our empirical study using several standard benchmarks and datasets show that Falcon significantly outperforms state-of-the-art entity and relation linking for short text query inventories.