메뉴 건너뛰기




Volumn 213, Issue 1-3, 2000, Pages 291-320

Edge isoperimetric inequalities for product graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0039980459     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(99)00189-2     Document Type: Article
Times cited : (26)

References (35)
  • 1
    • 0042142309 scopus 로고
    • Edge isoperimetric theorems for integer point arrays
    • R. Ahlswede, S. Bezrukov, Edge isoperimetric theorems for integer point arrays, Appl. Math. Lett. 8 (2) (1995) 75-80.
    • (1995) Appl. Math. Lett. , vol.8 , Issue.2 , pp. 75-80
    • Ahlswede, R.1    Bezrukov, S.2
  • 2
    • 33750994100 scopus 로고
    • 1, isoperimetric inequalities for graphs and superconcentrators
    • 1, isoperimetric inequalities for graphs and superconcentrators, J. Combin. Theory 38 (1985) 73-88.
    • (1985) J. Combin. Theory , vol.38 , pp. 73-88
    • Alon, N.1    Milman, V.D.2
  • 5
    • 0043144219 scopus 로고
    • Maximally connected arrays on the n-cube
    • A.J. Bernstein, Maximally connected arrays on the n-cube, SIAM J. Appl. Math. 15 (1967) 1485-1489.
    • (1967) SIAM J. Appl. Math. , vol.15 , pp. 1485-1489
    • Bernstein, A.J.1
  • 6
    • 0005363393 scopus 로고
    • Isoperimetric problems in discrete spaces
    • G. Katona, D. Miklos, P. Frankl, Z. Furedi (Eds.), Bolyai Society of Mathematical Studies Jànos Bolyai Mathematical Society, Budapest
    • S. Bezrukov, Isoperimetric problems in discrete spaces, in: G. Katona, D. Miklos, P. Frankl, Z. Furedi (Eds.), Extremal Problems for Finite Sets, Bolyai Society of Mathematical Studies 3, Jànos Bolyai Mathematical Society, Budapest, 1994, pp. 59-91.
    • (1994) Extremal Problems for Finite Sets , vol.3 , pp. 59-91
    • Bezrukov, S.1
  • 7
    • 0041641393 scopus 로고
    • preprint tri-ri-94-152 Fachbereich Mathematik-Informatik, Universität-Gesamthochschule Paderborn
    • S. Bezrukov, Variational principle in discrete extremal problems, preprint tri-ri-94-152 Fachbereich Mathematik-Informatik, Universität-Gesamthochschule Paderborn, 1994.
    • (1994) Variational Principle in Discrete Extremal Problems
    • Bezrukov, S.1
  • 9
    • 84972500849 scopus 로고
    • The spaces LP with mixed norms
    • A. Bennedek, R. Panzone, The spaces LP with mixed norms, Duke Math. J. 28 (1961) 301-324.
    • (1961) Duke Math. J. , vol.28 , pp. 301-324
    • Bennedek, A.1    Panzone, R.2
  • 10
    • 0005931492 scopus 로고
    • An isoperimetric inequality on the discrete torus
    • B. Bollobas, I. Leader, An isoperimetric inequality on the discrete torus, SIAM J. Discrete Math. 3 (1990) 32-37.
    • (1990) SIAM J. Discrete Math. , vol.3 , pp. 32-37
    • Bollobas, B.1    Leader, I.2
  • 11
    • 0000748606 scopus 로고
    • I. Leader, Edge-isoperimetric inequalities in the grid
    • B. Bollobas, I. Leader, Edge-isoperimetric inequalities in the grid, Combinatorica 11 (1991) 299-314.
    • (1991) Combinatorica , vol.11 , pp. 299-314
    • Bollobas, B.1
  • 12
    • 0001246517 scopus 로고
    • The isoperimetric number of random regular graphs
    • B. Bollobas, The isoperimetric number of random regular graphs, European J. Combin. 9 (1988) 241-244.
    • (1988) European J. Combin. , vol.9 , pp. 241-244
    • Bollobas, B.1
  • 13
    • 84974001919 scopus 로고
    • Modified isoperimetric constants, and large time heat diffusion in riemannian manifolds
    • I. Chavel, E.A. Feldman, Modified isoperimetric constants, and large time heat diffusion in riemannian manifolds, Duke Math. J. 64 (3) (1991) 473-499.
    • (1991) Duke Math. J. , vol.64 , Issue.3 , pp. 473-499
    • Chavel, I.1    Feldman, E.A.2
  • 15
    • 0038722452 scopus 로고    scopus 로고
    • Laplacians of graphs and Cheeger's inequalities
    • Paul Erdös is Eighty, Bolyai Mathematical Studies, Jànos Bolyai Mathematical Society, Budapest
    • F.R.K. Chung, Laplacians of graphs and Cheeger's inequalities, in: Combinatorics, Paul Erdös is Eighty, Vol. 2, Bolyai Mathematical Studies, Jànos Bolyai Mathematical Society, Budapest, 1996, pp. 157-172.
    • (1996) Combinatorics , vol.2 , pp. 157-172
    • Chung, F.R.K.1
  • 16
    • 0032400054 scopus 로고    scopus 로고
    • Isoperimetric inequalities for cartesian products of graphs
    • F.R.K. Chung, P. Tetali, Isoperimetric inequalities for cartesian products of graphs, Combin. Probab. Comput. 7 (1998) 141-148.
    • (1998) Combin. Probab. Comput. , vol.7 , pp. 141-148
    • Chung, F.R.K.1    Tetali, P.2
  • 17
    • 84974173398 scopus 로고
    • Eigenvalues of graphs and Sobolev inequalities
    • F.R.K. Chung, S.T. Yau, Eigenvalues of graphs and Sobolev inequalities, Combin. Probab. Comput. 4 (1995) 11-25.
    • (1995) Combin. Probab. Comput. , vol.4 , pp. 11-25
    • Chung, F.R.K.1    Yau, S.T.2
  • 18
    • 0001398283 scopus 로고
    • Difference equations, isoperimetric inequality and transience of certain random walks
    • J. Dodziuk, Difference equations, isoperimetric inequality and transience of certain random walks, Trans. Amer. Math. Soc. 24 (1984) 787-794.
    • (1984) Trans. Amer. Math. Soc. , vol.24 , pp. 787-794
    • Dodziuk, J.1
  • 19
    • 0000562793 scopus 로고
    • Normal and integral currents
    • H. Federer, W.H. Fleming, Normal and integral currents, Ann. Math. 72 (3) (1960) 458-520.
    • (1960) Ann. Math. , vol.72 , Issue.3 , pp. 458-520
    • Federer, H.1    Fleming, W.H.2
  • 20
    • 0000037976 scopus 로고
    • On the second eigenvalue and random walks in random d-regular graphs
    • J. Friedman, On the second eigenvalue and random walks in random d-regular graphs, Combinatorica 11 (4) (1991) 331-362.
    • (1991) Combinatorica , vol.11 , Issue.4 , pp. 331-362
    • Friedman, J.1
  • 21
    • 84974003380 scopus 로고
    • Some geometric aspects of graphs and their eigenfunctions
    • J. Friedman, Some geometric aspects of graphs and their eigenfunctions, Duke Math. J. 69 (3) (1993) 487-525.
    • (1993) Duke Math. J. , vol.69 , Issue.3 , pp. 487-525
    • Friedman, J.1
  • 23
    • 0001429116 scopus 로고
    • Logarithmic Sobolev inequalities
    • L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math. 97 (1975) 1061-1083.
    • (1975) Amer. J. Math. , vol.97 , pp. 1061-1083
    • Gross, L.1
  • 24
    • 0002236459 scopus 로고
    • Logarithmic Sobolev inequalities and contractivity properties of semi-groups
    • Springer, Berlin
    • L. Gross, Logarithmic Sobolev Inequalities and Contractivity Properties of Semi-groups, Lecture Notes in Mathematics, vol. 1563, Springer, Berlin, 1993, pp. 54-82.
    • (1993) Lecture Notes in Mathematics , vol.1563 , pp. 54-82
    • Gross, L.1
  • 25
    • 0001394447 scopus 로고
    • Optimal assignments of numbers to vertices
    • L.H. Harper, Optimal assignments of numbers to vertices, SIAM J. Appl. Math. 12 (1964) 131-135.
    • (1964) SIAM J. Appl. Math. , vol.12 , pp. 131-135
    • Harper, L.H.1
  • 26
    • 0000748659 scopus 로고
    • A note on the edges of the n-cube
    • S. Hart, A note on the edges of the n-cube, Discrete Math. 12 (1976) 157-163.
    • (1976) Discrete Math. , vol.12 , pp. 157-163
    • Hart, S.1
  • 27
    • 0041641358 scopus 로고
    • On a problem of Kleitman and West
    • L.H. Harper, On a problem of Kleitman and West, Discrete Math. 93 (1991) 169-182.
    • (1991) Discrete Math. , vol.93 , pp. 169-182
    • Harper, L.H.1
  • 29
    • 0039266344 scopus 로고
    • Assignments of numbers to vertices
    • J.H. Lindsey, Assignments of numbers to vertices, Amer. Math. Monthly 71 (1964) 508-516.
    • (1964) Amer. Math. Monthly , vol.71 , pp. 508-516
    • Lindsey, J.H.1
  • 30
    • 0001649842 scopus 로고
    • Isoperimetric numbers of graphs
    • B. Mohar, Isoperimetric numbers of graphs, J. Combin. Theory Ser. B 47 (1989) 274-291.
    • (1989) J. Combin. Theory Ser. B , vol.47 , pp. 274-291
    • Mohar, B.1
  • 31
    • 84968517521 scopus 로고
    • Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators
    • O. Rothaus, Logarithmic Sobolev inequalities and the spectrum of Sturm-Liouville operators, J. Funct Anal. 39 (1980) 42-56.
    • (1980) J. Funct Anal. , vol.39 , pp. 42-56
    • Rothaus, O.1
  • 32
    • 0000247778 scopus 로고
    • Diffusion on compact riemannian manifolds and logarithmic Sobolev inequalities
    • O. Rothaus, Diffusion on compact riemannian manifolds and logarithmic Sobolev inequalities, J. Funct. Anal. 42 (1981) 102-109.
    • (1981) J. Funct. Anal. , vol.42 , pp. 102-109
    • Rothaus, O.1
  • 33
    • 0000665059 scopus 로고
    • Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
    • O. Rothaus, Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities, J. Funct. Anal. 64 (1985) 296-313.
    • (1985) J. Funct. Anal. , vol.64 , pp. 296-313
    • Rothaus, O.1
  • 34
    • 84974122218 scopus 로고
    • On canonical current flows, crossing number, and graph expansion
    • F. Shahrokhi, L. Székely, On canonical current flows, crossing number, and graph expansion, Combin. Probab. Comput. 3 (1994) 523-543.
    • (1994) Combin. Probab. Comput. , vol.3 , pp. 523-543
    • Shahrokhi, F.1    Székely, L.2
  • 35
    • 46549090570 scopus 로고
    • Isoperimetric inequalities and Markov chains
    • N.Th. Varopoulos, Isoperimetric inequalities and Markov chains, J. Funct. Anal. 63 (1985) 215-239.
    • (1985) J. Funct. Anal. , vol.63 , pp. 215-239
    • Varopoulos, N.Th.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.