Geodesic
Competition hypergraphs of digraphs with certain properties I. Strong connectedness
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 5-21

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If D = (V,A) is a digraph, its competition hypergraph (D) has the vertex set V and e ⊆ V is an edge of (D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that e = w ∈ V|(w,v) ∈ A. We tackle the problem to minimize the number of strong components in D without changing the competition hypergraph (D). The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [3].
Keywords: hypergraph, competition graph, strong component 
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Sonntag, Martin; Teichert, Hanns-Martin. Competition hypergraphs of digraphs with certain properties I. Strong connectedness. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 5-21. http://geodesic.mathdoc.fr/item/DMGT_2008_28_1_a0/