메뉴 건너뛰기




Volumn 28, Issue 3, 2002, Pages 313-330

Isoperimetric constants of infinite plane graphs

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036026062     PISSN: 01795376     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00454-002-0694-2     Document Type: Article
Times cited : (21)

References (19)
  • 2
    • 20344362744 scopus 로고
    • A lower bound for the smallest eigenvalue of the Laplacian
    • [C], Princeton University Press, Princeton, NJ
    • [C] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, in Problems in Analysis, A Symposium in Honor of S. Bochner, pp. 195-199, Princeton University Press, Princeton, NJ, 1970.
    • (1970) Problems in Analysis, A Symposium in Honor of S. Bochner , pp. 195-199
    • Cheeger, J.1
  • 3
    • 0012962459 scopus 로고
    • 2-cohomology of noncompact surfaces
    • [De]
    • 2-cohomology of noncompact surfaces, Trans. Amer. Math. Soc. 284 (1984), 543-565.
    • (1984) Trans. Amer. Math. Soc. , vol.284 , pp. 543-565
    • Debaun, D.R.1
  • 4
    • 0001398283 scopus 로고
    • Difference equations, isoperimetric inequality and transience of certain random walks
    • [Do]
    • [Do] J. Dodziuk, Difference equations, isoperimetric inequality and transience of certain random walks, Trans. Amer. Math. Soc. 284 (1984), 787-794.
    • (1984) Trans. Amer. Math. Soc. , vol.284 , pp. 787-794
    • Dodziuk, J.1
  • 5
    • 0003195390 scopus 로고
    • Hyperbolic groups
    • [G], Springer-Verlag, New York
    • M. Gromov, Hyperbolic groups, in Essays in Group Theory, pp. 75-263, Springer-Verlag, New York, 1987.
    • (1987) Essays in Group Theory , pp. 75-263
    • Gromov, M.1
  • 6
    • 84986478042 scopus 로고
    • Edge-transitive planar graphs
    • [GS]
    • [GS] B. Grünbaum and G. C. Shephard, Edge-transitive planar graphs, J. Graph Theory 11 (1987), 141-155.
    • (1987) J. Graph Theory , vol.11 , pp. 141-155
    • Grünbaum, B.1    Shephard, G.C.2
  • 7
    • 0035993055 scopus 로고    scopus 로고
    • Explicit isoperimetric constants and phase transitions in the random-cluster model
    • [HJL]
    • [HJL] O. Häggström, J. Jonasson, and R. Lyons, Explicit isoperimetric constants and phase transitions in the random-cluster model, Ann. Probab. 30 (2002), 443-473.
    • (2002) Ann. Probab. , vol.30 , pp. 443-473
    • Häggström, O.1    Jonasson, J.2    Lyons, R.3
  • 9
    • 38249030408 scopus 로고
    • Isoperimetric inequalities, growth and the spectrum of graphs
    • [M1]
    • [M1] B. Mohär, Isoperimetric inequalities, growth and the spectrum of graphs, Linear Algebra Appl. 103 (1988), 119-131.
    • (1988) Linear Algebra Appl. , vol.103 , pp. 119-131
    • Mohär, B.1
  • 10
    • 38249032783 scopus 로고
    • Embeddings of infinite graphs
    • [M2]
    • [M2] B. Mohar, Embeddings of infinite graphs, J. Combin. Theory Ser. B 44 (1988), 29-43.
    • (1988) J. Combin. Theory Ser. B , vol.44 , pp. 29-43
    • Mohar, B.1
  • 11
    • 0001649842 scopus 로고
    • Isoperimetric numbers of graphs
    • [M3]
    • [M3] 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
  • 12
    • 0001622378 scopus 로고
    • Isoperimetric numbers and spectral radius of some infinite planar graphs
    • [M4]
    • [M4] B. Mohar, Isoperimetric numbers and spectral radius of some infinite planar graphs, Math. Slovaca 42 (1992), 411-425.
    • (1992) Math. Slovaca , vol.42 , pp. 411-425
    • Mohar, B.1
  • 13
    • 0007805173 scopus 로고
    • A survey on spectra of infinite graphs
    • [MW]
    • [MW] B. Mohär and W. Woess, A survey on spectra of infinite graphs, Bull. London Math. Soc. 21 (1989), 209-234.
    • (1989) Bull. London Math. Soc. , vol.21 , pp. 209-234
    • Mohär, B.1    Woess, W.2
  • 14
    • 33646607148 scopus 로고    scopus 로고
    • Genus bounds for embeddings with large connectivity and representativity
    • [PZ]
    • [PZ] M. D. Plummer and X. Zha, Genus bounds for embeddings with large connectivity and representativity, Discrete Math. 249 (2002), 167-178.
    • (2002) Discrete Math. , vol.249 , pp. 167-178
    • Plummer, M.D.1    Zha, X.2
  • 16
    • 0001726384 scopus 로고
    • Recurrence and transience of the edge graph of a tiling of the Euclidean plane
    • [S]
    • [S] P. M. Soardi, Recurrence and transience of the edge graph of a tiling of the Euclidean plane, Math. Ann. 287 (1990), 613-626.
    • (1990) Math. Ann. , vol.287 , pp. 613-626
    • Soardi, P.M.1
  • 17
    • 22444453472 scopus 로고    scopus 로고
    • A note on tilings and strong isoperimetric inequality
    • [W]
    • [W] W. Woess, A note on tilings and strong isoperimetric inequality, Math. Proc. Cambridge Philos. Soc. 124 (1998), 385-393.
    • (1998) Math. Proc. Cambridge Philos. Soc. , vol.124 , pp. 385-393
    • Woess, W.1
  • 18
    • 0000100131 scopus 로고
    • Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold
    • [Y]
    • [Y] S. T. Yau, Isoperimetric constants and the first eigenvalue of a compact Riemannian manifold, Ann. Sci. École Nom. Sup. (4) 8 (1975), 487-507.
    • (1975) Ann. Sci. École Nom. Sup. , vol.8 , Issue.4 , pp. 487-507
    • Yau, S.T.1
  • 19
    • 0031316034 scopus 로고    scopus 로고
    • On the norms of the random walks on planar graphs
    • [Z]
    • [Z] A. Zuk, On the norms of the random walks on planar graphs, Ann. Inst. Fourier (Grenoble) 47 (1997), 1463-1490.
    • (1997) Ann. Inst. Fourier (Grenoble) , vol.47 , pp. 1463-1490
    • Zuk, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.