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Vizing’s conjecture: A two-thirds bound for claw-free graphs. (English) Zbl 1368.05113
Summary: We show that for any claw-free graph $$G$$ and any graph $$H$$, $$\gamma(G \square H) \geq \frac{2}{3} \gamma(G) \gamma(H)$$, where $$\gamma(G)$$ is the domination number of $$G$$.

##### MSC:
 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C76 Graph operations (line graphs, products, etc.)
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##### References:
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