Competition hypergraphs of digraphs with certain properties I. Strong connectedness

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].