To address the complexity of hypergraph-related problems, several authors have proposed alternative structures for representing hypergraphs. Although these new representations may improve the understanding of such problems, their associated computational complexity often remains NP-hard. In addition, some authors have developed algorithms tailored to specific types of hypergraphs. In this study, we introduce a novel representation of simple, undirected hypergraphs using the concept of a reduced graph. This representation preserves the high-level relationships of the original hypergraph while enabling the design of efficient algorithms for specific hypergraph classes. We demonstrate that this structure is particularly useful for computing minimal transversals of minimum cardinality as well as minimal transversals of maximum cardinality. Furthermore, we present a simple algorithm to compute the latter for irredundant hypergraphs.
Rodriguez-Puente et al. (Fri,) studied this question.