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Domination in Graphs of Minimum Degree Five

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Abstract

Let G=(V,E) be a simple graph. A subset D⊆V is a dominating set of G, if for any vertex x ∈ V−D, there exists a vertex y ∈ D such that xy ∈ E. By using the so-called vertex disjoint paths cover introduced by Reed, 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.

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Authors and Affiliations

  1. Dept. of Mathematics, Langfang Teachers College, Langfang, Hebei, 065000, People's Republic of China

    Hua-Ming Xing

  2. Dept. of Mathematics, Beijing Institute of Technology, Beijing, 100081, People's Republic of China

    Liang Sun

  3. Dept. of Mathematics, Shantou University, Santou, Guangdong, 515063, People's Republic of China

    Xue-Gang Chen

Authors
  1. Hua-Ming Xing
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  2. Liang Sun
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  3. Xue-Gang Chen
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Xing, HM., Sun, L. & Chen, XG. Domination in Graphs of Minimum Degree Five. Graphs and Combinatorics 22, 127–143 (2006). https://doi.org/10.1007/s00373-006-0638-3

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  • DOI: https://doi.org/10.1007/s00373-006-0638-3

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