Competition hypergraphs of digraphs with certain properties I. Strong connectedness
Martin Sonntag, Hanns‐Martin Teichert · Discussiones Mathematicae Graph Theory · 2008
If D = (V, A) is a digraph, its competition hypergraph CH(D) has the vertex set V and e ⊆ V is an edge of CH(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 CH(D).The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [3].