Random procedures for dominating sets in bipartite graphs

Artmann, Sarah Dr.rer.nat.; Harant, Jochen

doi:10.7151/dmgt.1494

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2019

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Cited by 2 publications

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“…A deterministic algorithm to construct a dominating set satisfying the bound of Theorem 1 can be found in [1]. Using the same procedure of Alon and Spencer for the proof of Theorem 1, similar upper bounds for several domination variants have been obtained, (see, for example, [3,4,6,7,8,9,10,11]. Caro and Roditty [5,11] gave the following upper bound for the domination number of a graph which is one of the strongest known upper bounds for the domination number.…”

Section: Introductionmentioning

confidence: 95%

New Probabilistic Upper Bounds on the Domination Number of a Graph

Rad

2019

Electron. J. Combin.

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A subset $S$ of vertices of a graph $G$ is a dominating set of $G$ if every vertex in $V(G)-S$ has a neighbor in $S$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. In this paper, we obtain new (probabilistic) upper bounds for the domination number of a graph, and improve previous bounds given by Arnautov (1974), Payan (1975), and Caro and Roditty (1985) for any graph, and Harant, Pruchnewski and Voigt (1999) for regular graphs.

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