A color-exchange algorithm for exact graph coloring

  • Thomas J. Sager
  • Shi-Jen Lin
Track1: Graph Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 507)


DEXCH, a color-exchange exact graph coloring algorithm is presented. On many classes of graphs, DEXCH can, in the mean, find the chromatic number of a graph considerably faster than the DSATUR algorithm. The improvement over DSATUR stems from the ability to reorganize the subset of colored vertices and to detect in certain instances the existence of a complete subgraph of cardinality equal to the number of colors used in the best coloring found so far. The mean improvement over DSATUR is greatest on high edge-density graphs attaining the value of 42% on random graphs of edge-density 0.7 on 64 vertices.


algorithms branch-and-bound chromatic number graph-coloring NP-Complete scheduling 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Brelaz, D.: New methods to color vertices of a graph. Comm. ACM, 22, 4, Apr. 1979, pp251–256.zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    Garey, M.R. and D.S. Johnson: The complexity of near-optimal graph coloring. J. ACM, 23, 1, Jan. 1976, pp43–49.zbMATHMathSciNetCrossRefGoogle Scholar
  3. [3]
    Johnson, D.S., C.R. Aragon, L.A. McGeoch and C. Schevon: Optimization by simulated annealing: an experimental evaluation, Part II (graph coloring and number partitioning). Manuscript, 1989.Google Scholar
  4. [4]
    Johri, A. and D.W. Matula: Probabilistic bounds and heuristic algorithms for coloring large random graphs. Tech. Rep. 82-CSE-6, Southern Methodist University, Dallas, Tex., June 1982.Google Scholar
  5. [5]
    Korman, S.M.: The graph coloring problem. In Combinatorial Optimization, Eds. N. Christofides et al., Wiley, New York, 1979, pp211–235.Google Scholar
  6. [6]
    Kubale, M. and B. Jackowski: A general implicit enumeration algorithm for graph coloring. Comm. ACM, 28, 4, April 1985, pp412–418.CrossRefGoogle Scholar
  7. [7]
    Leighton, F.T.: A graph coloring algorithm for large scheduling problems. J. Res. Nat. Bur. Standards, 84, 6, Nov. 1979, pp489–506.zbMATHMathSciNetGoogle Scholar
  8. [8]
    Park, S.K. and K.W. Miller: Random number generators: good ones are hard to find. Comm. ACM, 31, 10, Oct. 1988, pp1192–1201.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Sager, T.J. and S.J. Lin: An improved exact graph coloring algorithm. Tech. Rep. CSc-89-1, University of Missouri-Rolla, Rolla, Missouri, April 1989.Google Scholar
  10. [10]
    Sager, T.J. and S.J. Lin: A pruning procedure for exact graph coloring. Tech. Rep. CSc-89-3, University of Missouri-Rolla, Rolla, Missouri, October 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Thomas J. Sager
    • 1
  • Shi-Jen Lin
    • 2
  1. 1.Department of Computer ScienceUniversity of Missouri-RollaRollaUSA
  2. 2.Department of Computer ScienceChung-Yung UniversityChung-LiTaiwan

Personalised recommendations