图论导引PDF电子书下载

1.Introduction 1

1.1.Graphs and Graph Models 1

1.2.Connected Graphs 9

1.3.Common Classes of Graphs 19

1.4.Multigraphs and Digraphs 26

2.Degrees 31

2.1.The Degree of a Vertex 31

2.2.Regular Graphs 38

2.3.Degree Sequences 43

2.4.Excursion：Graphs and Matrices 48

2.5.Exploration：Irregular Graphs 50

3.Isomorphic Graphs 55

3.1.The Definition of Isomorphism 55

3.2.Isomorphism as a Relation 63

3.3.Excursion：Graphs and Groups 66

3.4.Excursion：Reconstruction and Solvability 76

4.Trees 85

4.1.Bridges 85

4.2.Trees 87

4.3.The Minimum Spanning Tree Problem 94

4.4.Excursion：The Number of Spanning Trees 101

5.Connectivity 107

5.1.Cut-Vertices 107

5.2.Blocks 111

5.3.Connectivity 115

5.4.Menger’s Theorem 124

5.5.Exploration：Geodetic Sets 130

6.Traversability 133

6.1.Eulerian Graphs 133

6.2.Hamiltonian Graphs 140

6.3.Exploration：Hamiltonian Walks and Numbers 152

6.4.Excursion：The Early Books of Graph Theory 156

7.Digraphs 161

7.1.Strong Digraphs 161

7.2.Tournaments 169

7.3.Excursion：Decision-Making 176

7.4.Exploration：Wine Bottle Problems 180

8.Matchings and Factorization 183

8.1.Matchings 183

8.2.Factorization 194

8.3.Decompositions and Graceful Labelings 209

8.4.Excursion：Instant Insanity 214

8.5.Excursion：The Petersen Graph 219

8.6.Exploration：γ-Labelings of Graphs 224

9.Planarity 227

9.1.Planar Graphs 227

9.2.Embedding Graphs on Surfaces 241

9.3.Excursion：Graph Minors 249

9.4.Exploration：Embedding Graphs in Graphs 253

10.Coloring 259

10.1.The Four Color Problem 259

10.2.Vertex Coloring 267

10.3.Edge Coloring 280

10.4.Excursion：The Heawood Map Coloring Theorem 288

10.5.Exploration：Local Coloring 293

11.Ramsey Numbers 297

11.1.The Ramsey Number of Graphs 297

11.2.Turan’s Theorem 307

11.3.Exploration：Rainbow Ramsey Numbers 314

11.4.Excursion：Erdos Numbers 321

12.Distance 327

12.1.The Center of a Graph 327

12.2.Distant Vertices 333

12.3.Excursion：Locating Numbers 341

12.4.Excursion：Detour and Directed Distance 346

12.5.Exploration：Channel Assignment 351

12.6.Exploration：Distance Between Graphs 357