A Branch-and-Bound Procedure for the Largest Clique in a Graph

  • Earl R. Barnes
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 42)


We describe an algorithm for computing upper and lower bounds on the size of the largest clique in a graph. This algorithm is then incorporated in a branch-and-bound procedure for determining the largest clique exactly.


Adjacency Matrix Cholesky Factorization Maximum Clique Problem Large Clique Constant Weight Code 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. W. Carter, G. Laporte, J.W. Chinneck, “A general examination scheduling system”, Interfaces, Vol. 24, No. 3, 1994, pp. 109–120.Google Scholar
  2. [2]
    F. T. Leighton, “A graph coloring algorithm for large scheduling problems”, Journal of Research of the National Bureau of Standards, Vol. 84, 1979, pp. 489–506.MathSciNetMATHGoogle Scholar
  3. [3]
    A.E. Brouwer, J. B. Shearer, N.J.A. Sloane, and W.D. Smith, “A new table of constant weight codes”, IEEE Transactions on Information Theory, Vol. 36, 1990, pp. 1334–1380.Google Scholar
  4. [4]
    H. Ogawa, “Labeled point pattern matching by Delaunay triangulation and maximal cliques”, Pattern Recognition, Vol. 19, No. 1, 1986, pp. 35–40.CrossRefGoogle Scholar
  5. [5]
    P.M. Pardalos and J. Xue, “The maximum clique problem”, Journal of Global Optimzation, Vol. 4, 1994, pp. 301–328.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    T.S. Motskin and E.G. Strauss, “Maxima for graphs and a new proof of a theorem of Turan”, Canadian Journal of Mathematics, Vol. 17, No. 4, 1965, pp. 533–540.Google Scholar
  7. [7]
    L.E. Gibbons, D.W. Hearn, P.M. Pardalos, and M.V. Ramana, “Continuous characterization of the maximum clique problem”, Mathematics of Operations Research, Vol 22, No. 3, 1997, pp. 754–768.Google Scholar
  8. [8]
    L.E. Gibbons, D.W. Hearn, and P.M. Pardalos, “A continuous based heuristic for the maximum clique problem”, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 26, 1996, pp. 103–124.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Earl R. Barnes
    • 1
  1. 1.School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations