Geodesic
Sum labellings of cycle hypergraphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 255-265

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A hypergraph is a sum hypergraph iff there are a finite S ⊆ IN⁺ and d̲, [d̅] ∈ IN⁺ with 1 d̲ ≤ [d̅] such that is isomorphic to the hypergraph _d̲,[d̅] (S) = (V,) where V = S and = e ⊆ S:d̲ ≤ |e| ≤ [d̅] ∧ ∑_v∈ e v ∈ S. For an arbitrary hypergraph the sum number σ = σ() is defined to be the minimum number of isolated vertices y₁,..., y_σ ∉ V such that ∪ y₁,...,y_σ is a sum hypergraph.
Keywords: hypergraphs, sum number, vertex labelling 
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Teichert, Hanns-Martin. Sum labellings of cycle hypergraphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 2, pp. 255-265. http://geodesic.mathdoc.fr/item/DMGT_2000_20_2_a8/