Strengthening the Lovász θ (Ḡ) bound for graph coloring

Mathematical Programming

Volumn 102, Issue 3, 2005, Pages 577-588

  Meurdesoif, Philippe ^a  

^a UNIVERSITÉ BORDEAUX 1   (France)

Author keywords

Combinatorial optimization; Graph coloring; Lov sz number; SDP relaxation

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMIZATION; POLYNOMIALS; SET THEORY;

COMBINATORIAL OPTIMIZATION; GRAPH COLORING; LOVÁSZ Θ NUMBER; SDP RELAXATION;

GRAPH THEORY;

EID: 17444380875     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s101070100246     Document Type: Article

References (16)

1. Alizadeh, F., Haeberly, J.-P. Nayakkankuppam, M.V., Overton, M.L. (1997): SDPPack User's Guide, version 0.8 beta. Technical report, NYU Computer Science Dpt, March 1997 URL: http://www.cs.nyu.edu/phd_students/madhu/sdppack/sdppack. html
2. Alon, N. (1994): Explicit Ramsey graphs and orthonormal labelings. Electron. J. Comb. 1, # R12
3. Alon, N., Kahale, N. (1998): Approximating the independence number via the θ-function. Math. Program. 80, 253-264
4. Feige, U., Kilian, J. (1996): Zero Knowledge and the Chromatic Number. In: Proceedings of the 11th Annual IEEE Conference in Computing Complexity (preliminary version), pp. 278-287
5. Frieze, A., Jerrum, M. (1995): Improved approximation algorithms for MAX k-cut and MAX BISECTION. In: Proceedings of the Fourth MPS Conference on Integer Programming and Combinatorial Optimization. Springer
6. Goemans, M.X., Williamson, D.P. (1995): Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming. J. ACM 42, 1115-1145
7. Horn, R.A., Johnson, C.R. (1985): Matrix Analysis. Cambridge University Press, Cambridge (reedited 1999)
8. Jensen, T.R., Toft, B. (1995): Graph coloring problems. Wiley-Interscience series in discrete mathematics and optimization. Wiley, New York
9. Karger, D., Motwani, R., Sudan, M. (1998): Approximate graph coloring by semidefinite programming. J. ACM 45 (2), 246-265, March 1998
10. Knuth, D. (1994): The Sandwich Theorem. Electron. J. Comb. 1, # A1, 48 pp.
11. Lemaréchal, C., Oustry, F. (1999): Semidefinite relaxations and Lagrangian duality with application to combinatorial optimization. Rapport de Recherche Nr. 3710. Inria
12. Lovász, L. (1979): On the Shannon Capacity of a Graph. IEEE Trans. Inf. Theory IT-25 (1), 1-7
13. Lund, C., Yannakakis, M. (1994): On the hardness of approximating minimization problems. J. ACM 41 (5), 960-981
14. McEliece, R.J., Rodemich, E.R., Rumsey Jr., H.C. (1978): The Lovász Bound and Some Generalizations. J. Comb. Inf. Syst. Sci. 3 (3), 134-152
15. Poljak, S., Rendl, F., Wolkowicz, H. (1995): A recipe for semidefinite relaxation for (0 - 1)-quadratic programming. J. Glob. Optim. 7, 51-73
16. Schrijver, A. (1979): A Comparison of the Delsarte and Lovász Bounds. IEEE Trans. Inf. Theory IT-25 (4), 425-429