On the notion of cycles in hypergraphs

The notion of hypergraph cyclicity is crucial in numerous fields of application of hypergraph theory (e.g. in computer science, in relational database theory and constraint programming). Surprisingly, while this notion has been well studied during last thirty years, no relevant definition of cycles in hypergraphs has been proposed by the community. In this paper, we propose a definition of cycles in hypergraphs, αα-cycle based on the same principle in graph theory, meaning that a hypergraph is acyclic iff it does not contain an αα-cycle. This result completes the theory of the mostly used notion of hypergraph acyclicity, the αα-acyclicity.