数学研究生教材:图论(第3版)

数学研究生教材:图论(第3版)
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作者: [德]
2008-03
版次: 1
ISBN: 9787506291859
定价: 49.00
装帧: 平装
开本: 16开
纸张: 胶版纸
页数: 410页
正文语种: 简体中文,英语
51人买过
  •   Almosttwodecadeshavepassedsincetheappearanceofthosegraphtheorytextsthatstillsettheagendaformostintroductorycoursestaughttoday.Thecanoncreatedbythosebookshashelpedtoidentifysomemainfieldsofstudyandresearch,andwilldoubtlesscontinuetoinfluencethedevelopmentofthedisciplineforsometimetocome.
      Yetmuchhashappenedinthose20years,ingraphtheorynolessthanelsewhere:deepnewtheoremshavebeenfound,seeminglydisparatemethodsandresultshavebecomeinterrelated,entirenewbrancheshavearisen.Tonamejustafewsuchdevelopments,onemaythinkofhowthenewnotionoflistcolouringhasbridgedthegulfbetweeninvuriantssuchasaveragedegreeandchromaticnumber,howprobabilisticmethodsandtheregularitylemmahavepervadedextremaigraphtheoryandRamseytheory,orhowtheentirelynewfieldofgraphminorsandtree-decompositionshasbroughtstandardmethodsofsurfacetopologytobearonlong-standingalgorithmicgraphproblems. Preface
    1TheBasics
    1.1Graphs
    1.2Thedegreeofavertex
    1.3Pathsandcycles
    1.4Connectivity
    1.5Treesandforests
    1.6Bipartitegraphs
    1.7Contractionandminors
    1.8Eulertours
    1.9Somelinearalgebra
    1.10Othernotionsofgraphs
    Exercises
    Notes

    2Matching,CoveringandPacking
    2.1Matchinginbipartitegraphs
    2.2Matchingingeneralgraphs
    2.3Packingandcovering
    2.4Tree-packingandarboricity
    2.5Pathcovers
    Exercises
    Notes

    3Connectivity
    3.12-Connectedgraphsandsubgraphs..
    3.2Thestructureof3-connectedgraphs
    3.3Mengerstheorem
    3.4Maderstheorem
    3.5Linkingpairsofvertices
    Exercises
    Notes
    4PlanarGr
    aphs
    4.1Topologicalprerequisites
    4.2Planegraphs
    4.3Drawings
    4.4Planargraphs:Kuratowskistheorem.
    4.5Algebraicplanaritycriteria
    4.6Planeduality
    Exercises
    Notes

    5Colouring
    5.1Colouringmapsandplanargraphs
    5.2Colouringvertices
    5.3Colouringedges
    5.4Listcolouring
    5.5Perfectgraphs
    Exercises
    Notes

    6Flows
    6.1Circulations
    6.2Flowsinnetworks
    6.3Group-valuedflows
    6.4k-Flowsforsmallk
    6.5Flow-colouringduality
    6.6Tuttesflowconjectures
    Exercises
    Notes
    7ExtremalGraphTheory
    8InfiniteGraphs
    9RamseyTheoryforGraphs
    10HamiltonCycles
    11RandomGrapnhs
    12MionorsTreesandWQO
  • 内容简介:
      Almosttwodecadeshavepassedsincetheappearanceofthosegraphtheorytextsthatstillsettheagendaformostintroductorycoursestaughttoday.Thecanoncreatedbythosebookshashelpedtoidentifysomemainfieldsofstudyandresearch,andwilldoubtlesscontinuetoinfluencethedevelopmentofthedisciplineforsometimetocome.
      Yetmuchhashappenedinthose20years,ingraphtheorynolessthanelsewhere:deepnewtheoremshavebeenfound,seeminglydisparatemethodsandresultshavebecomeinterrelated,entirenewbrancheshavearisen.Tonamejustafewsuchdevelopments,onemaythinkofhowthenewnotionoflistcolouringhasbridgedthegulfbetweeninvuriantssuchasaveragedegreeandchromaticnumber,howprobabilisticmethodsandtheregularitylemmahavepervadedextremaigraphtheoryandRamseytheory,orhowtheentirelynewfieldofgraphminorsandtree-decompositionshasbroughtstandardmethodsofsurfacetopologytobearonlong-standingalgorithmicgraphproblems.
  • 目录:
    Preface
    1TheBasics
    1.1Graphs
    1.2Thedegreeofavertex
    1.3Pathsandcycles
    1.4Connectivity
    1.5Treesandforests
    1.6Bipartitegraphs
    1.7Contractionandminors
    1.8Eulertours
    1.9Somelinearalgebra
    1.10Othernotionsofgraphs
    Exercises
    Notes

    2Matching,CoveringandPacking
    2.1Matchinginbipartitegraphs
    2.2Matchingingeneralgraphs
    2.3Packingandcovering
    2.4Tree-packingandarboricity
    2.5Pathcovers
    Exercises
    Notes

    3Connectivity
    3.12-Connectedgraphsandsubgraphs..
    3.2Thestructureof3-connectedgraphs
    3.3Mengerstheorem
    3.4Maderstheorem
    3.5Linkingpairsofvertices
    Exercises
    Notes
    4PlanarGr
    aphs
    4.1Topologicalprerequisites
    4.2Planegraphs
    4.3Drawings
    4.4Planargraphs:Kuratowskistheorem.
    4.5Algebraicplanaritycriteria
    4.6Planeduality
    Exercises
    Notes

    5Colouring
    5.1Colouringmapsandplanargraphs
    5.2Colouringvertices
    5.3Colouringedges
    5.4Listcolouring
    5.5Perfectgraphs
    Exercises
    Notes

    6Flows
    6.1Circulations
    6.2Flowsinnetworks
    6.3Group-valuedflows
    6.4k-Flowsforsmallk
    6.5Flow-colouringduality
    6.6Tuttesflowconjectures
    Exercises
    Notes
    7ExtremalGraphTheory
    8InfiniteGraphs
    9RamseyTheoryforGraphs
    10HamiltonCycles
    11RandomGrapnhs
    12MionorsTreesandWQO
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