# Sum labellings of cycle hypergraphs

Discussiones Mathematicae Graph Theory (2000)

- Volume: 20, Issue: 2, page 255-265
- ISSN: 2083-5892

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topHanns-Martin Teichert. "Sum labellings of cycle hypergraphs." Discussiones Mathematicae Graph Theory 20.2 (2000): 255-265. <http://eudml.org/doc/270630>.

@article{Hanns2000,

abstract = {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.
Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this class of cycle hypergraphs.},

author = {Hanns-Martin Teichert},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {hypergraphs; sum number; vertex labelling; sum hypergraph; sum labellings},

language = {eng},

number = {2},

pages = {255-265},

title = {Sum labellings of cycle hypergraphs},

url = {http://eudml.org/doc/270630},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Hanns-Martin Teichert

TI - Sum labellings of cycle hypergraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2000

VL - 20

IS - 2

SP - 255

EP - 265

AB - 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.
Generalizing the graph Cₙ we obtain d-uniform hypergraphs where any d consecutive vertices of Cₙ form an edge. We determine sum numbers and investigate properties of sum labellings for this class of cycle hypergraphs.

LA - eng

KW - hypergraphs; sum number; vertex labelling; sum hypergraph; sum labellings

UR - http://eudml.org/doc/270630

ER -

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