A lower bound on the independence number of a graph in terms of degrees

• Autorzy: Jochen Harant , Ingo Schiermeyer
• Języki publikacji: EN

Abstrakty

EN

For a connected and non-complete graph, a new lower bound on its independence number is proved. It is shown that this bound is realizable by the well known efficient algorithm MIN.

Słowa kluczowe

EN

independence; stability; algorithm

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques
• 05C85: Graph algorithms

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 3
• Strony: 431-437

Daty

wydano

2006

otrzymano

2005-11-28

poprawiono

2006-06-28

Twórcy

autor

Jochen Harant

• Institut für Mathematik, TU Ilmenau, 98684 Ilmenau, Germany

autor

Ingo Schiermeyer

• Institut für Diskrete Mathematik und Algebra, TU Bergakademie Freiberg, 09596 Freiberg, Germany

Bibliografia

• [1] E. Bertram and P. Horak, Lower bounds on the independence number, Geombinatorics V (1996) 93-98.
• [2] Y. Caro, New results on the independence number (Technical Report. Tel-Aviv University, 1979).
• [3] Y. Caro and Z. Tuza, Improved lower bounds on k-independence, J. Graph Theory 15 (1991) 99-107, doi: 10.1002/jgt.3190150110.
• [4] S. Fajtlowicz, On the size of independent sets in graphs, 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] 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.
• [7] J. Harant and I. Schiermeyer, On the independence number of a graph in terms of order and size, Discrete Math. 232 (2001) 131-138, doi: 10.1016/S0012-365X(00)00298-3.
• [8] 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.
• [9] 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.
• [10] 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.
• [11] 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.
• [12] 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.1335