Classes of hypergraphs with sum number one
Hanns-Martin Teichert
Discussiones Mathematicae Graph Theory, Tome 20 (2000), p. 93-103 / Harvested from The Polish Digital Mathematics Library
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A hypergraph ℋ is a sum hypergraph iff there are a finite S ⊆ ℕ⁺ and d̲,d̅ ∈ ℕ⁺ with 1 < d̲ < d̅ such that ℋ is isomorphic to the hypergraph ℋd̲,d̅(S)=(V,) where V = S and =e⊆S:d̲<|e|<d̅∧∑v∈ev∈S. For an arbitrary hypergraph ℋ the sum number(ℋ ) is defined to be the minimum number of isolatedvertices w₁,...,wσ∉V such that ℋ∪w₁,...,wσ is a sum hypergraph. For graphs it is known that cycles Cₙ and wheels Wₙ have sum numbersgreater than one. Generalizing these graphs we prove for the hypergraphs ₙ and ₙ that under a certain condition for the edgecardinalities (ₙ)= (ₙ)=1

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:270220 
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Hanns-Martin Teichert. Classes of hypergraphs with sum number one. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 93-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1109/

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