Keyword search is an alternative for structured languages in querying graph-structured data. A result to a keyword query is a connected structure covering all or part of the queried keywords. The textual coverage and structural compactness have been known as the two main properties of a relevant result to a keyword query. Many previous works examined these properties after retrieving all of the candidate results using a ranking function in a comparative manner. However, this needs a time-consuming search process, which is not appropriate for an interactive system in which the user expects results in the least possible time. This problem has been addressed in recent works by confining the shape of results to examine their coverage and compactness during the search. However, these methods still suffer from the existence of redundant nodes in the retrieved results. In this paper, we introduce the semantic of minimal covered r-clique (MCCr) for the results of a keyword query as an extended model of existing definitions. We propose some efficient algorithms to detect the MCCrs of a given query. These algorithms can retrieve a comprehensive set of non-duplicate MCCrs in response to a keyword query. In addition, these algorithms can be executed in a distributive manner, which makes them outstanding in the field of keyword search. We also propose the approximate versions of these algorithms to retrieve the top-k approximate MCCrs in a polynomial delay. It is proved that the approximate algorithms can retrieve results in two-approximation. Extensive experiments on two real-world datasets confirm the efficiency and effectiveness of the proposed algorithms.