数学研究生教材：图论（第3版）

图书标准信息

• 作者 [德]迪斯特尔 著
• 出版社 世界图书出版公司
• 出版时间 2008-03
• 版次 1
• ISBN 9787506291859
• 定价 49.00元
• 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

【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