| Summary: | This paper aims at studying the relationship between two rather relevant theoretic fields such as Graph Theory and Testor Theory, deepening in the unexploited relation between the concepts of Minimal Transversal and Irreducible Testor. First, the classic definitions of each concept are provided, and then the relation between them is shown and formalized. Some of the immediate consequences of this relation, in terms of the duality property of transversals and about the equivalence of the result of two specific algorithms, one from each field, are discussed. Finally, we also discuss several future research directions that arise from the relationship between the concepts of Minimal Transversal And Irreducible Testor, and the way in which those directions can potentially benefit the development of theory and algorithms for solving different practical problems in both areas.
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