A spectral technique for coloring random 3-colorable graphs

SIAM Journal on Computing

Volumn 26, Issue 6, 1997, Pages 1733-1748

  Alon, Noga ^a,b   Kahale, Nabil ^c  

^a INSTITUTE FOR ADVANCED STUDY   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

^c LUCENT TECHNOLOGIES   (United States)

Author keywords

Algorithms; Graph coloring; Graph eigenvalues; Random graphs

Indexed keywords

EID: 0001690318     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794270248     Document Type: Article

References (19)

1. B. ASPVALL AND J. R. GILBERT, Graph coloring using eigenvalue decomposition, SIAM J. Alg. Discrete Meth., 5 (1984), pp. 526-538.
2. N. ALON AND J. H. SPENCER, The Probabilistic Method, John Wiley, New York, 1991.
3. A. BLUM, Some, tools for approximate 3-coloring, in Proc. 31st IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1990, pp. 554-562.
4. B. BOLLOBÁS, Random Graphs, Academic Press, New York, 1985.
5. 3/14)-coloring algorithm for 3-colorable graphs, Inform. Process. Lett., 61 (1997), pp. 49-53.
6. A. BLUM AND J. H. SPENCER, Coloring random and semi-random k-colorable graphs, J. Algorithms, 19 (1995), pp. 204-234.
7. R. BOPPANA, Eigenvalues and graph bisection: An average case analysis, in Proc. 28th IEEE Symposium on the Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1987, pp. 280-285.
8. M. E. DYER AND A. M. FRIEZE, The solution of some random NP-hard problems in polynomial expected time, J. Algorithms, 10 (1989), pp. 451-489.
9. J. FRIEDMAN, On the second eigenvalue and random walks in random d-regular graphs, Combinatorica, 11 (1991), pp. 331-362.
10. Z. FÜREDI AND J. KOMLÓS, The eigenvalues of random symmetric matrices, Combinatorica, 1 (1981), pp. 233-241.
11. J. FRIEDMAN, J. KAHN, AND E. SZEMEREDI, On the second eigenvalue in random regular graphs, in Proc. 21st ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1989, pp. 587-598.
12. M. R. GAREY AND D. S. JOHNSON, Computers and Intractability: A Guide to the Theory of NP-completeness, W. H. Freeman, San Francisco, 1979.
13. R. KARP, Reducibility Among Combinatorial Problems, R. E. Miller and J. W. Thatcher, eds., Plenum Press, New York, 1972.
14. D. KARGER, R. MOTWANI, AND M. SUDAN, Approximate graph coloring by semidefinite programming, in Proc. 35th IEEE Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA, 1994, pp. 2-13.
15. L. KUCERA, Expected behavior of graph colouring algorithms, in Lecture Notes Comput. Sci. 56, Springer-Verlag, New York, 1977, pp. 447-451.
16. A. D. PETFORD AND D. J. A. WELSH, A randomised 3-colouring algorithm, Discrete Math., 74 (1989), pp. 253-261.
17. A. RALSTON, A First Course in Numerical Analysis, McGraw-Hill, New York, 1985, Section 10.4.
18. J. S. TURNER, Almost all k-colorable graphs are easy to color, J. Algorithms, 9 (1988), pp. 63-82.
19. J. H, WILKINSON, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965.