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Graph Theory Third Edition【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

Graph Theory Third Edition
  • Reinhard Diestel 著
  • 出版社： Springer
  • ISBN：3540261826
  • 出版时间：2005
  • 标注页数：416页
  • 文件大小：44MB
  • 文件页数：435页
  • 主题词：

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图书目录

1.The Basics1

1.1 Graphs2

1.2 The degree of a vertex5

1.3 Paths and cycles6

1.4 Connectivity10

1.5 Trees and forests13

1.6 Bipartite graphs17

1.7 Contraction and minors18

1.8 Euler tours22

1.9 Some linear algebra23

1.10 Other notions of graphs28

Exercises30

Notes32

2.Matching，Covering and Packing33

2.1 Matching in bipartite graphs34

2.2 Matching in general graphs（*）39

2.3 Packing and covering44

2.4 Tree-packing and arboricity46

2.5 Path covers49

Exercises51

Notes53

3.Connectivity55

3.1 2-Connected graphs and subgraphs55

3.2 The structure of 3-connected graphs（*）57

3.3 Menger’s theorem62

3.4 Mader’s theorem67

3.5 Linking pairs of vertices（*）69

Exercises78

Notes80

4.Planar Graphs83

4.1 Topological prerequisites84

4.2 Plane graphs86

4.3 Drawings92

4.4 Planar graphs：Kuratowski’s theorem96

4.5 Algebraic planarity criteria101

4.6 Plane duality103

Exercises106

Notes109

5.Colouring111

5.1 Colouring maps and planar graphs112

5.2 Colouring vertices114

5.3 Colouring edges119

5.4 List colouring121

5.5 Perfect graphs126

Exercises133

Notes136

6.Flows139

6.1 Circulations（*）140

6.2 Flows in networks141

6.3 Group-valued flows144

6.4 k-Flows for small k149

6.5 Flow-colouring duality152

6.6 Tntte’s flow conjectures156

Exercises160

Notes161

7.Extremal Graph Theory163

7.1 Subgraphs164

7.2 Minors（*）169

7.3 Hadwiger’s conjecture172

7.4 Szemeredi’s regularity lemma175

7.5 Applying the regularity lemma183

Exercises189

Notes192

8.Infinite Graphs195

8.1 Basic notions，facts and techniques196

8.2 Paths，trees，and ends（*）204

8.3 Homogeneous and universal graphs212

8.4 Connectivity and matching216

8.5 The topological end space226

Exercises237

Notes244

9.Ramsey Theory for Graphs251

9.1 Ramsey’s original theorems252

9.2 Ramsey numbers（*）255

9.3 Induced Ramsey theorems258

9.4 Ramsey properties and connectivity（*）268

Exercises271

Notes272

10.Hamilton Cycles275

10.1 Simple sufficient conditions275

10.2 Hamilton cycles and degree sequences278

10.3 Hamilton cycles in the square of a graph281

Exercises289

Notes290

11.Random Graphs293

11.1 The notion of a random graph294

11.2 The probabilistic method299

11.3 Properties of almost all graphs302

11.4 Threshold functions and second moments306

Exercises312

Notes313

12.Minors，Trees and WQO315

12.1 Well-quasi-ordering316

12.2 The graph minor theorem for trees317

12.3 Tree-decompositions319

12.4 Tree-width and forbidden minors327

12.5 The graph minor theorem（*）341

Exercises350

Notes354

A.Infinite sets357

B.Surfaces361

Hints for all the exercises369

Index393

Symbol index409

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