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Graph Theory - Graduate Texts in Mathematics - 5th edition (2016)

Graph Theory - Graduate Texts in Mathematics - 5th edition (2016)

of: Reinhard Diestel

Springer-Diestel, 2016

ISBN: 9783961340057 , 444 Pages

5. Edition

Format: PDF, Read online

Copy protection: DRM

Mac OSX,Windows PC Apple iPad, Android Tablet PC's Read Online for: Mac OSX,Windows PC,Linux

Price: 12,99 EUR



More of the content

Graph Theory - Graduate Texts in Mathematics - 5th edition (2016)


 

Title page

1

Preface

4

About the second edition

7

About the third edition

8

About the fourth edition

10

About the fifth edition

11

Contents

12

1. The Basics

16

1.1 Graphs

17

1.2 The degree of a vertex

20

1.3 Paths and cycles

21

1.4 Connectivity

25

1.5 Trees and forests

28

1.6 Bipartite graphs

32

1.7 Contraction and minors

34

1.8 Euler tours

37

1.9 Some linear algebra

38

1.10 Other notions of graphs

42

Exercises

45

Notes

48

2. Matching, Covering and Packing

50

2.1 Matching in bipartite graphs

51

2.2 Matching in general graphs

56

2.3 The Erdös-Pósa theorem

60

2.4 Tree packing and arboricity

63

2.5 Path covers

67

Exercises

68

Notes

71

3. Connectivity

74

3.1 2-Connected graphs and subgraphs

74

3.2 The structure of 3-connected graphs

77

3.3 Menger’s theorem

82

3.4 Mader’s theorem

87

3.5 Linking pairs of vertices

89

Exercises

97

Notes

100

4. Planar Graphs

104

4.1 Topological prerequisites

105

4.2 Plane graphs

107

4.3 Drawings

113

4.4 Planar graphs: Kuratowski’s theorem

117

4.5 Algebraic planarity criteria

122

4.6 Plane duality

125

Exercises

128

Notes

132

5. Colouring

134

5.1 Colouring maps and planar graphs

135

5.2 Colouring vertices

137

5.3 Colouring edges

142

5.4 List colouring

144

5.5 Perfect graphs

150

Exercises

157

Notes

161

6. Flows

164

6.1 Circulations

165

6.2 Flows in networks

166

6.3 Group-valued flows

169

6.4 k-Flows for small k

174

6.5 Flow-colouring duality

177

6.6 Tutte’s flow conjectures

180

Exercises

184

Notes

186

7. Extremal Graph Theory

188

7.1 Subgraphs

189

7.2 Minors

195

7.3 Hadwiger’s conjecture

198

7.4 Szemerédi’s regularity lemma

202

7.5 Applying the regularity lemma

210

Exercises

216

Notes

219

8. Infinite Graphs

224

8.1 Basic notions, facts and techniques

225

8.2 Paths, trees, and ends

234

8.3 Homogeneous and universal graphs

243

8.4 Connectivity and matching

246

8.5 Recursive structures

257

8.6 Graphs with ends: the complete picture

260

8.7 The topological cycle space

269

8.8 Infinite graphs as limits of finite ones

273

Exercises

276

Notes

288

9. Ramsey Theory for Graphs

298

9.1 Ramsey’s original theorems

299

9.2 Ramsey numbers

302

9.3 Induced Ramsey theorems

305

9.4 Ramsey properties and connectivity

315

Exercises

318

Notes

319

10. Hamilton Cycles

322

10.1 Sufficient conditions

322

10.2 Hamilton cycles and degree sequences

326

10.3 Hamilton cycles in the square of a graph

329

Exercises

334

Notes

335

11. Random Graphs

338

11.1 The notion of a random graph

339

11.2 The probabilistic method

344

11.3 Properties of almost all graphs

347

11.4 Threshold functions and second moments

350

Exercises

357

Notes

359

12. Minors, Trees, and WQO

362

12.1 Well-quasi-ordering

363

12.2 The graph minor theorem for trees

364

12.3 Tree-decompositions

366

12.4 Tree-width

370

12.5 Tangles

375

12.6 Tree-decompositions and forbidden minors

384

12.7 The graph minor theorem

389

Exercises

397

Notes

403

Appendix A: Infinite sets

408

Appendix B: Surfaces

414

Hints for the Exercises

422

Index

424

Symbol Index

442