Competition hypergraphs of digraphs with certain properties II. Hamiltonicity

If D = (V,A) is a digraph, its competition hypergraph CH(D) has 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 = N− D (v) = {w ∈ V |(w, v) ∈ A}. We give characterizations of CH(D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ -cycle factor. The results are closely related to the corresponding investigations for competition graphs in K.F.Fraughnaugh et al., Competition graphs of strongly connected and hamiltonian digraphs; SIAM J. Discr. Math. 8 (1995), 179-185 and D.R. Guichard, Competition graphs of hamiltonian digraphs; SIAM J. Discr. Math. 11 (1998), 128–134.