On Vizing's conjecture
Bostjan Bresar
Discussiones Mathematicae Graph Theory, Tome 21 (2001), p. 5-11 / Harvested from The Polish Digital Mathematics Library
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A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)-D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G ⃞ H Vizing's conjecture [10] states that γ(G ⃞ H) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:270337 
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Bostjan Bresar. On Vizing's conjecture. Discussiones Mathematicae Graph Theory, Tome 21 (2001) pp. 5-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1129/

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