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A d-uniform hypergraph H is a sum hypergraph iff there is a finite

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 = {w ∈ V |(w, v) ∈ A}. For several products D 1 • D 2 of digraphs D 1 and D 2 , we investigate the relations between the competition hypergraphs of the factors D 1 , D 2 and the competition… (More)

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… (More)

Let G = (V, E) be a simple undirected graph. N (G) = (V, E N) is the neighborhood graph of the graph G, if and only if E N = {{a, b} | a = b ∧ ∃ x ∈ V : {x, a} ∈ E ∧ {x, b} ∈ E}. After discussing several structural properties of N (G), e.g. edge numbers and connectivity, we characterize the hamiltonicity of N (G) by means of chords of a hamiltonian cycle in… (More)

A hypergraph H is a sum hypergraph iff there are a finite S ⊆ IN + and d, d ∈ IN + with 1 < d ≤ d such that H is isomorphic to the hypergraph H d,d (S) = (V, E) where V = S and E = {e ⊆ S : d ≤ |e| ≤ d ∧ v∈e v ∈ S}. For an arbitrary hypergraph H the sum number σ = σ(H) is defined to be the minimum number of isolated vertices w 1 ,. .. , w σ ∈ V such that H… (More)