On domination in graphs

• Autorzy: Frank Göring , Jochen Harant
• Języki publikacji: EN

Abstrakty

EN

For a finite undirected graph G on n vertices two continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the domination number γ of G. An efficient approximation method is developed and known upper bounds on γ are slightly improved.

Słowa kluczowe

EN

graph; domination

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 1-2
• Strony: 7-12

Daty

wydano

2005

otrzymano

2003-09-23

poprawiono

2004-06-15

Twórcy

autor

Frank Göring

• Department of Mathematics, Chemnitz University of Technology, D-09107 Chemnitz, Germany

autor

Jochen Harant

• Department of Mathematics, Technical University of Ilmenau, D-98684 Ilmenau, Germany

Bibliografia

• [1] Y. Caro, New results on the independence number (Technical Report, Tel-Aviv University, 1979).
• [2] Y. Caro and Zs. Tuza, Improved lower bounds on k-independence, J. Graph Theory 15 (1991) 99-107, doi: 10.1002/jgt.3190150110.
• [3] R. Diestel, Graph Theory, Graduate Texts in Mathematics (Springer, 1997).
• [4] N. Alon, J.H. Spencer and P. Erdös, The Probabilistic Method (John Wiley and Sons, Inc. 1992), page 6.
• [5] M.R. Garey and D.S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness (W.H. Freeman and Company, San Francisco, 1979).
• [6] J. Harant, Some news about the independence number of a graph, Discuss. Math. Graph Theory 20 (2000) 71-79, doi: 10.7151/dmgt.1107.
• [7] J. Harant, A. Pruchnewski and M. Voigt, On dominating sets and independent sets of graphs, Combinatorics, Probability and Computing 8 (1999) 547-553, doi: 10.1017/S0963548399004034.
• [8] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, Inc., New York, N.Y., 1998), page 52.
• [9] V.K. Wei, A lower bound on the stability number of a simple graph (Bell Laboratories Technical Memorandum 81-11217-9, Murray Hill, NJ, 1981).

Identyfikatory

DOI

10.7151/dmgt.1254