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A \(\frac{3}{4}\)-approximation of Vizing’s conjecture for claw-free graphs. (English) Zbl 1443.05138
Summary: Vizing’s conjecture [V. G. Vizing, Vychisl. Sistemy, Novosibirsk 9, 30–43 (1963; Zbl 0194.25203)] asserts that the domination number of the Cartesian product of two graphs is at least as large as the product of their domination numbers. We prove that for any claw-free graph \(G\) and an arbitrary graph \(H\), the inequality \(\gamma (G \square H) \geq \frac{3}{4} \gamma (G) \gamma (H)\) always holds.
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C76 Graph operations (line graphs, products, etc.)
Full Text: DOI
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