An elementary construction of constant-degree expanders

Combinatorics Probability and Computing

Volumn 17, Issue 3, 2008, Pages 319-327

  Alon, Noga ^a   Schwartz, Oded ^a   Shapira, Asaf ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

COMBINATORIAL MATHEMATICS; ITERATIVE METHODS; SPECTRUM ANALYSIS;

BOUNDED DEGREE EXPANDERS; ELEMENTARY CONSTRUCTION;

ANGLE MEASUREMENT;

EID: 42249105555     PISSN: 09635483     EISSN: 14692163     Source Type: Journal    
DOI: 10.1017/S0963548307008851     Document Type: Article

References (15)

1. Ajtai, M. (1994) Recursive construction for 3-regular expanders. Combinatorica 14 379-416.
2. Alon, N. (1986) Eigenvalues and expanders. Combinatorica 6 83-96.
3. Alon, N. and Milman, V. D. (1984) Eigenvalues, expanders and superconcentrators. In Proc. 25th Annual Symp. on Foundations of Computer Science (FOCS), Singer Island, Florida, IEEE, pp. 320-322.
4. 1, isoperimetric inequalities for graphs and superconcentrators. J. Combin. Theory Ser. B 38 73-88 (1985).
5. Alon, N. and Roichman, Y. (1994) Random Cayley graphs and expanders. Random Struct. Alg. 5 271-284.
6. Bilu, Y. and Linial, N. (2006) Lifts, discrepancy and nearly optimal spectral gaps. Combinatorica 26 495-519.
7. Dodziuk, J. (1984) Difference equations, isoperimetric inequality and transience of certain random walks. Trans. Amer. Math. Soc. 284 787-794.
8. Gabber, O. and Galil Z. (1981) Explicit constructions of linear-sized superconcentrators. J. Comput. Syst. Sci. 22 407-420.
9. Gromov, M. (1983) Filling Riemannian manifolds. J. Differential Geometry 18 1-147.
10. Hoory, S., Linial, N. and Wigderson, A. (2006) Expander graphs and their applications. Bull. Amer. Math. Soc. 43 439-561.
11. Lubotzky, A., Phillips, R. and Sarnak, P. (1988) Ramanujan graphs. Combinatorica 8 261-277.
12. Margulis, G. (1973) Explicit constructions of expanders. Problemy Peredacl Informacii 9 71-80.
13. Margulis, G. A. (1988) Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and superconcentrators. Problems of Information Transmission 24 39-46.
14. Pinsker, M. (1973) On the complexity of a concentrator. In 7th Annual Teletrqffic Conference, pp. 1-4.
15. Reingold, O., Vadhan S. and Wigderson, A. (2002) Entropy waves, the zig-zag graph product, and new constant-degree expanders. Ann. of Math. 155 157-187.