On the Laplacian eigenvalues of Gn,p

Combinatorics Probability and Computing

Volumn 16, Issue 6, 2007, Pages 923-946

  Coja Oghlan, Amin ^a  

^a CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY SEQUENCES; GRAPH THEORY; LAPLACE EQUATION; RANDOM PROCESSES;

LAPLACIAN SPECTRA; SUBGRAPHS;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 35348968289     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548307008693     Document Type: Article

References (26)

1. Alon, N. (1998) Spectral techniques in graph algorithms. In Proc. 3rd LATIN, pp. 206-215.
2. Alon, N. and Kahale, N. (1997) A spectral technique for coloring random 3-colorable graphs. SIAM J. Comput. 26 1733-1748.
3. Alon, N., Krivelevich, M. and Sudakov, B. (1998) Finding a large hidden clique in a random graph. Random Struct. Alg. 13 457-466.
4. Bauer, M. and Golinelli, O. (2001) Random incidence matrices: Moments of the spectral density. J. Statist. Phys. 103 301-337.
5. Bollobás, B. (2001) Random Graphs, 2nd edn, Springer.
6. Boppana, R. (1987) Eigenvalues and graph bisection: An average-case analysis. In Proc. 28th FOCS, pp. 280-285.
7. Chung, F. R. K. (1997) Spectral Graph Theory, AMS.
8. Chung, F. R. K., Lu, L. and Vu, V. (2003) The spectra of random graphs with given expected degrees. Internet Mathematics 1 257-275.
9. Coja-Oghlan, A. (2005) Spectral techniques, semidefinite programs, and random graphs. Habilitation thesis, Humboldt University, Berlin.
10. Coja-Oghlan, A. (2006) A spectral heuristic for bisecting random graphs. Random Struct. Alg. 29 351-398.
11. Dasgupta, A., Hopcroft, J. E. and McSherry, F. (2004) Spectral partitioning of random graphs. In Proc. 45th FOCS, pp. 529-537.
12. Donath, W. E. and Hoffman, A. J. (1973) Lower bounds for the partitioning of a graph. IBM J. Res. Develop. 17 420-425.
13. Feige, U. and Ofek, E. (2005) Spectral techniques applied to sparse random, graphs. Random Struct. Alg. 27 251-275.
14. Friedman, J. (2003) A proof of Alon's second eigenvalue conjecture. In Proc. 35th STOC, pp. 720-724.
15. Friedman, J., Kahn, J. and Szemerédi, E. (1989) On the second eigenvalue in random regular graphs. In Proc. 21st STOC, pp. 587-598.
16. Füredi, Z. and Komloś, J. (1981) The eigenvalues of random symmetric matrices. Combinatorica 1 233-241.
17. Golub, G. H. and van Loan, C. F. (1996) Matrix Computations, 3rd edn, Johns Hopkins University Press.
18. Guattery, S. and Miller, G. L. (1998) On the quality of spectral separators. SIAM J. Matrix Anal. Appl. 19 701-719.
19. Janson, S. (2005) The first eigenvalue of random graphs. Combin. Probab. Comput. 14 815-828.
20. Janson, S., Luczak, T. and Ruciński, A. (2000) Random Graphs, Wiley.
21. Khorunzhiy, O., Kirsch, W. and Müller, P. (2005) Lifshits tails for spectra of Erdos-Rerandom graphs. Annals of applied probability 16 (2006) 295-309. Preprint: arXiv:math-ph/0502054 v1.
22. Krivelevich, M. and Sudakov, B. (2003) The largest eigenvalue of sparse random graphs. Combin. Probab. Comput. 12 61-72.
23. Pothen, A., Simon, H. D. and Liou, K.-P. (1990) Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11 430-452.
24. Schloegel, K., Karypis, G. and Kumar, V. (2000) Graph partitioning for high performance scientific simulations. In CRPC Parallel Computation Handbook (J. Dongarra, I. Foster, G. Fox, K. Kennedy and A. White, eds), Morgan-Kaufmann.
25. Vu, V. (2005) Spectral norm of random matrices. In Proc. 37th STOC, pp. 423-430.
26. Wigner, E. P. (1958) On the distribution of the roots of certain symmetric matrices. Ann. of Math. 67 325-327.