λ1, Isoperimetric inequalities for graphs, and superconcentrators

Journal of Combinatorial Theory, Series B - Tập 38 Số 1 - Trang 73-88 - 1985
Noga Alon1, Vitali Milman2
1Massachusetts Institute of Technology,
2Tel-Aviv University

Tóm tắt

Từ khóa


Tài liệu tham khảo

Ajtai, 1983, Sorting in c log n parallel steps, Combinatorica, 3, 1, 10.1007/BF02579338

Alon, 1984

Alon, 1984, Eigenvalues, expanders and superconcentrators, 320

Amir, 1980, Unconditional and symmetric sets in n-dimensional normed spaces, Israel J. Math., 37, 3, 10.1007/BF02762864

D. Amir and V. D. Milman, A quantitative finite dimensional Krivine theorem, preprint.

Angluin, 1979, A note on a construction of Margulis, Inform. Process. Lett., 8, 17, 10.1016/0020-0190(79)90084-X

Anderson, 1971, Eigenvalues of the Laplacian of a Graph

Babai, 1979, Spectrum of Cayley graphs, J. Combin. Theory Ser. B, 27, 180, 10.1016/0095-8956(79)90079-0

Bussemaker, 1977, Cubic graphs on ≤ 14 vertices, J. Combin. Theory Ser. B, 23, 234, 10.1016/0095-8956(77)90034-X

Bussemaker, 1978, Graphs related to exceptional root systems, Vol. 18, 185

Biggs, 1974

Buser, 1984, On the bipartition of graphs, 9, 105

Cvetković, 1980

Cheeger, 1970, A lower bound for the smallest eigenvalue of the Laplacian, 195

Cvetković, 1981, Some possible directions in further investigations of graph spectra, 47

Donath, 1973, Lower bounds for the partitioning of graphs, IBM J. Res. Develop., 17, 420, 10.1147/rd.175.0420

Frankl, 1981, A short proof for a theorem of Harper about Hamming spheres, Discrete Math., 34, 311, 10.1016/0012-365X(81)90009-1

Fiedler, 1973, Algebraic connectivity of graphs, Czechoslovak. Math. J., 23, 298, 10.21136/CMJ.1973.101168

Gabber, 1981, Explicit construction of linear sized superconcentrators, J. Comput. Systems Sci., 22, 407, 10.1016/0022-0000(81)90040-4

Gromov, 1983, Filling riemannian manifolds, J. Differential Geom., 18, 1, 10.4310/jdg/1214509283

Gromov, 1983, A topological application of the isoperimetric inequality, Amer. J. Math., 105, 843, 10.2307/2374298

Harper, 1966, Optimal numberings and isoperimetric problems on graphs, J. Combin. Theory, 1, 385, 10.1016/S0021-9800(66)80059-5

Kazhdan, 1967, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl., 1, 63, 10.1007/BF01075866

Levy, 1951

Lovász, 1975, Spectra of graphs with transitive groups, Period. Math. Hungar., 6, 191, 10.1007/BF02018821

Lovász, 1979

Margulis, 1973, Explicit construction of concentrators, Problemi Peredaci Informacii, 9, 71

Maurey, 1979, Espaces de Banach: Construction de suites symétriques, C. R. Acad. Sci. Paris Ser. A-B, 288, A-679

V. D. Milman and G. Schechtman, “Asymptotic Theory of Normed Linear Spaces,” Lecture Notes in Mathematics, to appear.

Newman, 1972, 107

Ralston, 1965

Schechtman, 1982, Levy type inequality for a class of finite metric spaces, Vol. 939, 211

Shamir, 1983

Tanner, 1984, Explicit construction of concentrators from generalized n-gons, SIAM J. Algebraic Discrete Methods, 5, 287, 10.1137/0605030

Wang, 1977, Extremal configurations on a discrete torus and a generalization of the generalized Macauley theorem, SIAM J. Appl. Math., 33, 55, 10.1137/0133006

Zimmer, 1982, Ergodic theory, group representations, and rigidity, Bull. Amer. Math. Soc. (N.S.), 6, 383, 10.1090/S0273-0979-1982-15005-4