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DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR

  • Sohn, Moo-Young ;
  • Xudong, Yuan
  • Published : 2009.07.01

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)|.

Keywords

graphs;domination number

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  2. On the Structure of Dominating Graphs vol.33, pp.4, 2017, https://doi.org/10.1007/s00373-017-1792-5
  3. On dominating sets of maximal outerplanar and planar graphs vol.198, 2016, https://doi.org/10.1016/j.dam.2015.06.024
  4. Dominating plane triangulations vol.211, 2016, https://doi.org/10.1016/j.dam.2016.04.011
  5. Dominating sets in plane triangulations vol.310, pp.17-18, 2010, https://doi.org/10.1016/j.disc.2010.03.022