Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR

  • Sohn, Moo-Young (DEPARTMENT OF APPLIED MATHEMATICS CHANGWON NATIONAL UNIVERSITY) ;
  • Xudong, Yuan (DEPARTMENT OF MATHEMATICS GUANGXI NORMAL UNIVERSITY)
  • Published : 2009.07.01
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Abstract

A dominating set for a graph G is a set D of vertices of G such that every vertex of G not in D is adjacent to a vertex of D. Reed [11] considered the domination problem for graphs with minimum degree at least three. He showed that any graph G of minimum degree at least three contains a dominating set D of size at most $\frac{3}{8}$ |V (G)| by introducing a covering by vertex disjoint paths. In this paper, by using this technique, we show that every graph on n vertices of minimum degree at least four contains a dominating set D of size at most $\frac{4}{11}$ |V (G)|.

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References

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