DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR

Title & Authors
DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR
Sohn, Moo-Young; Xudong, Yuan;

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 $\small{\frac{3}{8}}$ |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 $\small{\frac{4}{11}}$ |V (G)|.
Keywords
graphs;domination number;
Language
English
Cited by
1.
Improved Upper Bounds on the Domination Number of Graphs With Minimum Degree at Least Five, Graphs and Combinatorics, 2016, 32, 2, 511
2.
On the Structure of Dominating Graphs, Graphs and Combinatorics, 2017, 33, 4, 665
3.
On dominating sets of maximal outerplanar and planar graphs, Discrete Applied Mathematics, 2016, 198, 164
4.
Dominating plane triangulations, Discrete Applied Mathematics, 2016, 211, 175
5.
Dominating sets in plane triangulations, Discrete Mathematics, 2010, 310, 17-18, 2221
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