메뉴 건너뛰기




Volumn 21, Issue 5, 2011, Pages 1117-1143

Metric Uniformization and Spectral Bounds for Graphs

Author keywords

Eigenvalues; excluded minors; planar graphs; spectral geometry

Indexed keywords


EID: 80053603441     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00039-011-0132-9     Document Type: Article
Times cited : (23)

References (52)
  • 1
    • 80053601181 scopus 로고
    • Crossing-Free Subgraphs, Theory and Practice of Combinatorics: A Collection of Articles Honoring Anton Kotzig on the Occasion of His Sixtieth Birthday
    • (A. Kotzig, A. Rosa, G. Sabidussi, J. Turgeon, eds.), North-Holland, Amsterdam
    • M. Ajtai, V. Chvátal, M. Newborn, E. Szemerédi, Crossing-Free Subgraphs, Theory and Practice of Combinatorics: A Collection of Articles Honoring Anton Kotzig on the Occasion of His Sixtieth Birthday" (A. Kotzig, A. Rosa, G. Sabidussi, J. Turgeon, eds.), Annals of Discrete Mathematics 12, North-Holland, Amsterdam (1982).
    • (1982) Annals of Discrete Mathematics , vol.12
    • Ajtai, M.1    Chvátal, V.2    Newborn, M.3    Szemerédi, E.4
  • 2
    • 51249173340 scopus 로고
    • Eigenvalues and expanders
    • Alon N.: Eigenvalues and expanders,. Combinatorica 6(2), 83-96 (1986).
    • (1986) Combinatorica , vol.6 , Issue.2 , pp. 83-96
    • Alon, N.1
  • 3
    • 0001690318 scopus 로고    scopus 로고
    • A spectral technique for coloring random 3-colorable graphs
    • Alon N., Kahale N.: A spectral technique for coloring random 3-colorable graphs,. SIAM Journal on Computing 26, 1733-1748 (1997).
    • (1997) SIAM Journal on Computing , vol.26 , pp. 1733-1748
    • Alon, N.1    Kahale, N.2
  • 4
    • 33750994100 scopus 로고
    • 1, isoperimetric inequalities for graphs, and superconcentrators
    • 1, isoperimetric inequalities for graphs, and superconcentrators. J. Comb. Theory Series B. 38, 73-88 (1985).
    • (1985) J. Comb. Theory Series B. , vol.38 , pp. 73-88
    • Alon, N.1    Milman, V.D.2
  • 10
    • 0038589165 scopus 로고    scopus 로고
    • The anatomy of a large-scale hypertextual web search engine
    • Brin S., Page L., The anatomy of a large-scale hypertextual web search engine. Computer Networks 30: 1-7 (1998), 107-117.
    • (1998) Computer Networks , vol.30
    • Brin, S.1    Page, L.2
  • 11
    • 51249170362 scopus 로고
    • Triangulations and moduli spaces of Riemann surfaces with group actions
    • Buser P., Seppälä M., Silhol R.: Triangulations and moduli spaces of Riemann surfaces with group actions,. Manuscripta Mathematica 8(2), 209-224 (1995).
    • (1995) Manuscripta Mathematica , vol.8 , Issue.2 , pp. 209-224
    • Buser, P.1    Seppälä, M.2    Silhol, R.3
  • 14
    • 20344362744 scopus 로고
    • A lower bound for the smallest eigenvalue of the Laplacian
    • (R. C. Gunning, ed.), Princeton University Press
    • J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, in "Problems in Analysis" (R. C. Gunning, ed.), Princeton University Press (1970), 195-199.
    • (1970) Problems in Analysis , pp. 195-199
    • Cheeger, J.1
  • 15
    • 84968468352 scopus 로고
    • Diameters and eigenvalues
    • Chung F. R.: Diameters and eigenvalues,. J. Amer. Math. Soc. 2, 187-196 (1989).
    • (1989) J. Amer. Math. Soc. , vol.2 , pp. 187-196
    • Chung, F.R.1
  • 16
    • 0001777623 scopus 로고
    • Finite-difference approach to the Hodge theory of harmonic forms
    • Dodziuk J.: Finite-difference approach to the Hodge theory of harmonic forms,. American Journal of Mathematics 98(1), 79-104 (1976).
    • (1976) American Journal of Mathematics , vol.98 , Issue.1 , pp. 79-104
    • Dodziuk, J.1
  • 18
    • 0011504283 scopus 로고
    • Algorithms for partitioning of graphs and computer logic based on eigenvectors of connection matrices
    • Donath W. E., Hoffman A. J.: Algorithms for partitioning of graphs and computer logic based on eigenvectors of connection matrices,. IBM Technical Disclosure Bulletin 15, 938-944 (1972).
    • (1972) IBM Technical Disclosure Bulletin , vol.15 , pp. 938-944
    • Donath, W.E.1    Hoffman, A.J.2
  • 19
    • 0015661138 scopus 로고
    • Lower bounds for the partitioning of graphs
    • Donath W. E., Hoffman A. J.: Lower bounds for the partitioning of graphs,. J. Res. Develop. 17, 420-425 (1073).
    • (1073) J. Res. Develop. , vol.17 , pp. 420-425
    • Donath, W.E.1    Hoffman, A.J.2
  • 20
    • 0001545727 scopus 로고    scopus 로고
    • Divide-and-conquer approximation algorithms via spreading metrics
    • Even G., Naor J., Rao S., Schieber B.: Divide-and-conquer approximation algorithms via spreading metrics,. J. ACM 47(4), 585-616 (2000).
    • (2000) J. ACM , vol.47 , Issue.4 , pp. 585-616
    • Even, G.1    Naor, J.2    Rao, S.3    Schieber, B.4
  • 22
    • 0001350119 scopus 로고
    • Algebraic connectivity of graphs
    • Fiedler M.: Algebraic connectivity of graphs,. Czechoslovak Mathematical Journal 23(98), 298-305 (1973).
    • (1973) Czechoslovak Mathematical Journal , vol.23 , Issue.98 , pp. 298-305
    • Fiedler, M.1
  • 23
    • 0003186094 scopus 로고
    • Eigenvectors of acyclic matrices
    • Fiedler M.: Eigenvectors of acyclic matrices,. Czechoslovak Mathematical Journal 25(100), 607-618 (1975).
    • (1975) Czechoslovak Mathematical Journal , vol.25 , Issue.100 , pp. 607-618
    • Fiedler, M.1
  • 24
    • 0000827674 scopus 로고
    • A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory
    • Fiedler M.: A property of eigenvectors of nonnegative symmetric matrices and its applications to graph theory,. Czechoslovak Mathematical Journal 25(100), 619-633 (1975).
    • (1975) Czechoslovak Mathematical Journal , vol.25 , Issue.100 , pp. 619-633
    • Fiedler, M.1
  • 26
    • 37349007342 scopus 로고    scopus 로고
    • Decomposition of a metric space by capacitors
    • (Special volume dedicated to L. Nirenberg)
    • A. Grigor'yan, S.-T. Yau, Decomposition of a metric space by capacitors, in "Proceedings of Symposia in Pure Mathematics (Special volume dedicated to L. Nirenberg)" 65 (1999), 39-75.
    • (1999) Proceedings of Symposia in Pure Mathematics , vol.65 , pp. 39-75
    • Grigor'yan, A.1    Yau, S.-T.2
  • 27
    • 0014869120 scopus 로고
    • An r-dimensional quadratic placement algorithm
    • Hall K. M.: An r-dimensional quadratic placement algorithm,. Management Science 17, 219-229 (1970).
    • (1970) Management Science , vol.17 , pp. 219-229
    • Hall, K.M.1
  • 28
    • 0003780715 scopus 로고
    • Addison-Wesley, Reading, MA
    • F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1994.
    • (1994) Graph Theory
    • Harary, F.1
  • 29
    • 0001005571 scopus 로고
    • Quatre propriétés isopérimétriques de membranes sphériques homogénes
    • Hersch J.: Quatre propriétés isopérimétriques de membranes sphériques homogénes,. C. R. Acad. Sci. Paris Sér. A-B 270, A1645-A1648 (1970).
    • (1970) C. R. Acad. Sci. Paris Sér. , vol.A-B 270 , pp. 1645-1648
    • Hersch, J.1
  • 30
    • 33747185440 scopus 로고    scopus 로고
    • Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus
    • Kelner J. A.: Spectral partitioning, eigenvalue bounds, and circle packings for graphs of bounded genus,. SIAM J. Comput. 35(4), 882-902 (2006).
    • (2006) SIAM J. Comput. , vol.35 , Issue.4 , pp. 882-902
    • Kelner, J.A.1
  • 32
    • 4243148480 scopus 로고    scopus 로고
    • Authoritative sources in a hyperlinked environment
    • Kleinberg J. M.: Authoritative sources in a hyperlinked environment,. Journal of the ACM. 46, 668-677 (1999).
    • (1999) Journal of the ACM. , vol.46 , pp. 668-677
    • Kleinberg, J.M.1
  • 33
    • 0002877399 scopus 로고
    • Upper bounds for eigenvalues of conformal metrics
    • Korevaar N.: Upper bounds for eigenvalues of conformal metrics,. J. Differential Geometry 37, 73-93 (1993).
    • (1993) J. Differential Geometry , vol.37 , pp. 73-93
    • Korevaar, N.1
  • 34
    • 0002144725 scopus 로고
    • The minimum Hadwiger number for graphs with a given mean degree of vertices
    • Kostochka A. V.: The minimum Hadwiger number for graphs with a given mean degree of vertices,. Metody Diskret. Analiz. 38, 37-58 (1982).
    • (1982) Metody Diskret. Analiz. , vol.38 , pp. 37-58
    • Kostochka, A.V.1
  • 35
    • 26844509176 scopus 로고    scopus 로고
    • Measured descent: a new embedding method for finite metrics
    • Krauthgamer R., Lee J. R., Mendel M., Naor A.: Measured descent: a new embedding method for finite metrics,. Geom. funct. anal. 15(4), 839-858 (2005).
    • (2005) Geom. Funct. Anal. , vol.15 , Issue.4 , pp. 839-858
    • Krauthgamer, R.1    Lee, J.R.2    Mendel, M.3    Naor, A.4
  • 36
    • 15544369683 scopus 로고    scopus 로고
    • Extending Lipschitz functions via random metric partitions
    • Lee J. R., Naor A.: Extending Lipschitz functions via random metric partitions,. Invent. Math. 160(1), 59-95 (2005).
    • (2005) Invent. Math. , vol.160 , Issue.1 , pp. 59-95
    • Lee, J.R.1    Naor, A.2
  • 39
    • 0018457301 scopus 로고
    • A separator theorem for planar graphs
    • Lipton R. J., Tarjan R. E.: A separator theorem for planar graphs,. SIAM J. of Appl. Math. 36, 177-189 (1979).
    • (1979) SIAM J. Of Appl. Math. , vol.36 , pp. 177-189
    • Lipton, R.J.1    Tarjan, R.E.2
  • 40
    • 0004505622 scopus 로고    scopus 로고
    • Geometric separators for finite-element meshes
    • electronic
    • Miller G. L., Teng S.-H., Thurston W., Vavasis S. A.: Geometric separators for finite-element meshes,. SIAM J. Sci. Comput. 19(2), 364-86 (1998) (electronic).
    • (1998) SIAM J. Sci. Comput , vol.19 , Issue.2 , pp. 364-386
    • Miller, G.L.1    Teng, S.-H.2    Thurston, W.3    Vavasis, S.A.4
  • 42
    • 38249020670 scopus 로고
    • Graph minors. VIII. A Kuratowski theorem for general surfaces
    • Robertson N., Seymour P. D.: Graph minors. VIII. A Kuratowski theorem for general surfaces,. J. Combin. Theory Ser. B 48(2), 255-288 (1990).
    • (1990) J. Combin. Theory Ser. B , vol.48 , Issue.2 , pp. 255-288
    • Robertson, N.1    Seymour, P.D.2
  • 43
    • 9144239509 scopus 로고    scopus 로고
    • Graph minors. XX. Wagner's conjecture
    • Robertson N., Seymour P. D.: Graph minors. XX. Wagner's conjecture,. J. Combin. Theory Ser. B 92(2), 325-357 (2004).
    • (2004) J. Combin. Theory Ser. B , vol.92 , Issue.2 , pp. 325-357
    • Robertson, N.1    Seymour, P.D.2
  • 45
    • 0024699930 scopus 로고
    • Approximative counting, uniform generation and rapidly mixing Markov chains
    • Sinclair A. J., Jerrum M. R.: Approximative counting, uniform generation and rapidly mixing Markov chains,. Information and Computation 82(1), 93-133 (1989).
    • (1989) Information and Computation , vol.82 , Issue.1 , pp. 93-133
    • Sinclair, A.J.1    Jerrum, M.R.2
  • 46
    • 33846251992 scopus 로고    scopus 로고
    • Spectral partitioning works: planar graphs and finite element meshes
    • Spielman D. A., Teng S.-H.: Spectral partitioning works: planar graphs and finite element meshes,. Linear Algebra Appl. 421(2-3), 284-305 (2007).
    • (2007) Linear Algebra Appl. , vol.421 , Issue.2-3 , pp. 284-305
    • Spielman, D.A.1    Teng, S.-H.2
  • 47
    • 84976013923 scopus 로고
    • An extremal function for contractions of graphs
    • Thomason A.: An extremal function for contractions of graphs,. Math. Proc. Cambridge Philos. Soc. 95(2), 261-265 (1984).
    • (1984) Math. Proc. Cambridge Philos. Soc. , vol.95 , Issue.2 , pp. 261-265
    • Thomason, A.1
  • 49
    • 0013277425 scopus 로고
    • Kreisausfüllungen der hyperbolischen ebene
    • Tóth L. F.: Kreisausfüllungen der hyperbolischen ebene,. Acta Mathematica Hungarica 4(1), 103-110 (1953).
    • (1953) Acta Mathematica Hungarica , vol.4 , Issue.1 , pp. 103-110
    • Tóth, L.F.1
  • 50
    • 33845337775 scopus 로고
    • Über eine Eigenschaft der ebenen Komplexe
    • Wagner K.: Über eine Eigenschaft der ebenen Komplexe,. Math. Ann. 114(1), 570-590 (1937).
    • (1937) Math. Ann. , vol.114 , Issue.1 , pp. 570-590
    • Wagner, K.1
  • 52
    • 0001991729 scopus 로고
    • Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds
    • Yang P., Yau S. T.: Eigenvalues of the Laplacian of compact Riemann surfaces and minimal submanifolds,. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4(7), 55-63 (1980).
    • (1980) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.4 , Issue.7 , pp. 55-63
    • Yang, P.1    Yau, S.T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.