A sequential elimination algorithm for computing bounds on the clique number of a graph

Discrete Optimization

Volumn 5, Issue 3, 2008, Pages 615-628

  Gendron, Bernard ^a   Hertz, Alain ^b,c   St Louis, Patrick ^a  

^a UNIVERSITÉ DE MONTRÉAL   (Canada)

^b ÉCOLE POLYTECHNIQUE DE MONTRÉAL   (Canada)

^c GERAD   (Canada)

Author keywords

Clique number; Upper and lower bounds

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; NUMBER THEORY; PROBLEM SOLVING;

CLIQUE NUMBER; SEQUENTIAL ELIMINATION ALGORITHMS; UPPER AND LOWER BOUNDS;

GRAPH THEORY;

EID: 44149084436     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2008.01.001     Document Type: Article

References (14)

1. M. Aouchiche, Comparaison automatisée d'invariants en théorie des graphes. Ph.D. Thesis, École polytechnique de Montréal, 2006
2. D. Applegate, D. Johnson, Dfmax source code in C. A World Wide Web page ftp://dimacs.rutgers.edu/pub/challenge/graph/solvers/
3. Bomze I.M., Budinich M., Pardalos P.M., and Pelillo M. In: Du D.Z., and Pardalos P.M. (Eds). The Maximum Clique Problem. Handbook of Combinatorial Optimization vol. 4 (1999), Kluwer Academic Publishers 1-74
4. Brélaz D. New methods to color the vertices of a graph. Communications of the ACM 22 4 (1979) 251-256
5. Galinier P., and Hertz A. A survey of local search methods for graph coloring. Computers and Operations Research 33 9 (2006) 2547-2562
6. Garey M.R., and Johnson D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness (1979), W. H. Freeman
7. Harant J., Ryjacek Z., and Schiermeyer I. Forbidden subgraphs and MIN-algorithm for independence number. Discrete Mathematics 256 1-2 (2002) 193-201
8. Hertz A., and de Werra D. Using tabu search for graph coloring. Computing 39 (1987) 345-351
9. In: Johnson D.S., and Trick M.A. (Eds). Cliques, Coloring, and Satisfiability - Second DIMACS Implementation challenge. DIMACS - Series in Discrete Mathematics and Theoretical Computer Science vol. 26 (1993), American Mathematical Society 11-13
10. Knuth D.E. The sandwich theorem. Electronic Journal of Combinatorics 1 (1994) 48
11. Lovász L. On the Shannon capacity of a graph. IEEE Transactions on Information Theory 25 1 (1979) 1-7
12. Pardalos P.M., and Xue J. The maximum clique problem. Journal of Global Optimization 4 3 (1994) 301-328
13. P. St-Louis, B. Gendron, J.A. Ferland, A penalty-evaporation heuristic in a decomposition method for the maximum clique problem, Working paper, Département d'informatique et de recherche opérationnelle, Université de Montréal, Canada
14. Szekeres G., and Wilf H.S. An inequality for the chromatic number of graphs. Journal of Combinatorial Theory 4 (1968) 1-3