Paired-domination of Cartesian products of graphs and rainbow domination.

*(English)*Zbl 1200.05154
Raspaud, André (ed.) et al., 7th international colloquium on graph theory, Hyeres, France, September 12–16, 2005. Amsterdam: Elsevier. Electronic Notes in Discrete Mathematics 22, 233-237 (2005).

Summary: The most famous open problem involving domination in graphs is Vizing’s conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. We investigate a similar problem for paired-domination, and obtain a lower bound in terms of product of domination number of one factor and 3-packing of the other factor. Some results are obtained by applying a new graph invariant called rainbow domination.

For the entire collection see [Zbl 1109.05013].

For the entire collection see [Zbl 1109.05013].

##### MSC:

05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |

05C76 | Graph operations (line graphs, products, etc.) |

05C15 | Coloring of graphs and hypergraphs |

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\textit{B. Brešar} et al., Electron. Notes Discrete Math. 22, 233--237 (2005; Zbl 1200.05154)

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##### References:

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