## Domination in graphs of minimum degree five.(English)Zbl 1091.05054

Summary: Let $$G = (V,E)$$ be a simple graph. A subset $$D$$ of $$V$$ is a dominating set of $$G$$, if for any vertex $$x \in V-D$$, there exists a vertex $$y \in D$$ such that $$xy \in E$$. By using the so-called vertex disjoint paths cover introduced by B. Reed [Comb. Probab. Comput. 5, 277–295 (1996; Zbl 0857.05052)], in this paper we prove that every graph $$G$$ on $$n$$ vertices with minimum degree at least five has a dominating set of order at most $$5n/14$$.

### MSC:

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

Zbl 0857.05052
Full Text:

### References:

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