JOURNAL BROWSE
Search
Advanced SearchSearch Tips
DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
DOMINATION IN GRAPHS OF MINIMUM DEGREE FOUR
Sohn, Moo-Young; Xudong, Yuan;
  PDF(new window)
 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 |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 |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  crossref(new windwow)
2.
Dominating plane triangulations, Discrete Applied Mathematics, 2016, 211, 175  crossref(new windwow)
3.
On dominating sets of maximal outerplanar and planar graphs, Discrete Applied Mathematics, 2016, 198, 164  crossref(new windwow)
4.
Dominating sets in plane triangulations, Discrete Mathematics, 2010, 310, 17-18, 2221  crossref(new windwow)
 References
1.
N. Alon and J. H. Spencer, The Probabilistic Method, Wiley-Interscience, New York, 1992

2.
Y. Caro and Y. Roditty, On the vertex-independence number and star decomposition of graphs, Ars Combin. 20 (1985), 167–180

3.
Y. Caro and Y. Roditty, A note on the k-domination number of a graph, Internat. J. Math. Math. Sci. 13 (1990), no. 1, 205–206 crossref(new window)

4.
G. Chartrand and L. Lesniak, Graphs and Digraphs, 3rd Edition, Chapman and Hall, London, 1996

5.
M. R. Garey and D. S. Johnson, Computers and intractability, A guide to the theory of NP-completeness. A Series of Books in the Mathematical Sciences. W. H. Freeman and Co., San Francisco, Calif., 1979

6.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998

7.
T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in Graphs, Marcel Dekker, Inc., New York, 1998

8.
W. McCuaig and B. Shepherd, Domination in graphs with minimum degree two, J. Graph Theory 13 (1989), no. 6, 749–762 crossref(new window)

9.
O. Ore, Theory of Graphs, American Mathematical Society Colloquium Publications, Vol. XXXVIII, American Mathematical Society, Providence, R.I. 1962

10.
C. Payan and N. H. Xuong, Domination-balanced graphs, J. Graph Theory 6 (1982), no. 1, 23–32 crossref(new window)

11.
B. A. Reed, Paths, stars and the number three, Combin. Probab. Comput. 5 (1996), no. 3, 277–295 crossref(new window)

12.
B. A. Reed, Paths, stars and the number three: the grunge, University of Waterloo, Technical Report, 1993

13.
L. A. Sanchis, Bounds related to domination in graphs with minimum degree two, J. Graph Theory 25 (1997), no. 2, 139–152 crossref(new window)