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On the Chromatic Number of Graphs

Author

Listed:
  • S. Butenko
  • P. Festa
  • P. M. Pardalos

Abstract

Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 0–1 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates graphs of known chromatic number by using the KKT optimality conditions of a related continuous nonlinear program.

Suggested Citation

  • S. Butenko & P. Festa & P. M. Pardalos, 2001. "On the Chromatic Number of Graphs," Journal of Optimization Theory and Applications, Springer, vol. 109(1), pages 69-83, April.
    • Handle: RePEc:spr:joptap:v:109:y:2001:i:1:d:10.1023_a:1017557620292
    DOI: 10.1023/A:1017557620292
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    References listed on IDEAS

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    1. David S. Johnson & Cecilia R. Aragon & Lyle A. McGeoch & Catherine Schevon, 1991. "Optimization by Simulated Annealing: An Experimental Evaluation; Part II, Graph Coloring and Number Partitioning," Operations Research, INFORMS, vol. 39(3), pages 378-406, June.
    2. de Werra, D., 1985. "An introduction to timetabling," European Journal of Operational Research, Elsevier, vol. 19(2), pages 151-162, February.
    3. Chams, M. & Hertz, A. & de Werra, D., 1987. "Some experiments with simulated annealing for coloring graphs," European Journal of Operational Research, Elsevier, vol. 32(2), pages 260-266, November.
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