图论导论 第5版 英文PDF电子书下载

Introduction 1

1 Definitions and examples 8

1.1 Definitions 8

1.2 Examples 18

1.3 Variations on a theme 22

1.4 Three puzzles 26

2 Paths and cycles 32

2.1 Connectivity 32

2.2 Eulerian graphs and digraphs 40

2.3 Hamiltonian graphs and digraphs 47

2.4 Applications 52

3 Trees 61

3.1 Properties of trees 61

3.2 Counting trees 65

3.3 More applications 70

4 Planarity 80

4.1 Planar graphs 80

4.2 Euler's formula 86

4.3 Dual graphs 91

4.4 Graphs on other surfaces 96

5 Colouring graphs 101

5.1 Colouring vertices 101

5.2 Chromatic polynomials 107

5.3 Colouring maps 111

5.4 The four-colour theorem 117

5.5 Colouring edges 122

6 Matching,marriage and Menger's theorem 128

6.1 Hall'smarriage theorem 128

6.2 Menger's theorem 134

6.3 Network flows 138

7 Matroids 145

7.1 Introduction to matroids 145

7 2 Examples of matroids 149

7 3 Matroids and graphs 152

Appendix 1：Algorithms 158

Appendix 2：Table of numbers 161

List of symbols 162

Bibliography 163

Solutions to selected exercises 166

Index 181