On Matrix Representations of Participation Constraints

We discuss the existence of matrix representations for generalised and minimum participation constraints which are frequently used in database design and conceptual modelling. Matrix representations, also known as Armstrong relations, have been studied in literature e.g. for functional dependencies and play an important role in example-based design and for the implication problem of database constraints. The major tool to achieve the results in this paper is a theorem of Hajnal and Szemerédi on the occurrence of clique graphs in a given graph.