ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 20(1) (2000) 71-79
DOI: 10.7151/dmgt.1107


Jochen Harant

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


For a finite undirected graph G on n vertices some continuous optimization problems taken over the n-dimensional cube are presented and it is proved that their optimum values equal the independence number of G.

Keywords: graph, independence.

1991 Mathematical Subject Classification: 05C35.


[1] E. Bertram, P. Horak, Lower bounds on the independence number, Geombinatorics, (V) 3 (1996) 93-98.
[2] R. Boppana, M.M. Halldorsson, Approximating maximum independent sets by excluding subgraphs, BIT 32 (1992) 180-196, doi: 10.1007/BF01994876.
[3] Y. Caro, New results on the independence number (Technical Report, Tel-Aviv University, 1979).
[4] S. Fajtlowicz, On the size of independent sets in graphs, in: Proc. 9th S-E Conf. on Combinatorics, Graph Theory and Computing (Boca Raton 1978) 269-274.
[5] S. Fajtlowicz, Independence, clique size and maximum degree, Combinatorica 4 (1984) 35-38, doi: 10.1007/BF02579154.
[6] M.R. Garey, D.S. Johnson, Computers and Intractability, A Guide to the Theory of NP-Completeness (W.H. Freeman and Company, San Francisco, 1979).
[7] M.M. Halldorsson, J. Radhakrishnan, Greed is good: Approximating independent sets in sparse and bounded-degree graphs, Algorithmica 18 (1997) 145-163, doi: 10.1007/BF02523693.
[8] J. Harant, A lower bound on the independence number of a graph, Discrete Math. 188 (1998) 239-243, doi: 10.1016/S0012-365X(98)00048-X.
[9] J. Harant, A. Pruchnewski, M. Voigt, On dominating sets and independent sets of graphs, Combinatorics, Probability and Computing 8 (1999) 547-553, doi: 10.1017/S0963548399004034.
[10] J. Harant, I. Schiermeyer, On the independence number of a graph in terms of order and size, submitted.
[11] T.S. Motzkin, E.G. Straus, Maxima for graphs and a new proof of a theorem of Turan, Canad. J. Math. 17 (1965) 533-540, doi: 10.4153/CJM-1965-053-6.
[12] O. Murphy, Lower bounds on the stability number of graphs computed in terms of degrees, Discrete Math. 90 (1991) 207-211, doi: 10.1016/0012-365X(91)90357-8.
[13] S.M. Selkow, The independence number of graphs in terms of degrees, Discrete Math. 122 (1993) 343-348, doi: 10.1016/0012-365X(93)90307-F.
[14] S.M. Selkow, A probabilistic lower bound on the independence number of graphs, Discrete Math. 132 (1994) 363-365, doi: 10.1016/0012-365X(93)00102-B.
[15] J.B. Shearer, A note on the independence number of triangle-free graphs, Discrete Math. 46 (1983) 83-87, doi: 10.1016/0012-365X(83)90273-X.
[16] J.B. Shearer, A note on the independence number of triangle-free graphs, II, J. Combin. Theory (B) 53 (1991) 300-307, doi: 10.1016/0095-8956(91)90080-4.
[17] 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).

Received 8 February 1999