人民邮电出版社优秀图书：图论导引(英文版) 图灵原版数学·统计学系列

图论导引(英文版)
图灵原版数学·统计学系列

【我要购买】【我来说两句】【在线阅读】【经销商订货】【样本阅读】	【作者】	[美] Gary Chartrand Ping Zhang	【编辑】	王丽萍
	【ISBN】	7-115-14834-1	【日期】	2006-6
	【版次】	1	【印次】	1
	【页数】	435页	【字数】	460千字
	【开本】	16	【定价】	49元
	【光盘】		【优惠价】	39.3元
	【资源】		【库存】	无

　　本书介绍了图论的常用主题，同时也包含一些尚需进一步研究或未解决的议题，用于激发学生的创新能力。全书共分13章，前3章介绍一些基础知识，后面章节介绍了树、连通性、可遍历性、子图、匹配和因子分解、可平面性、图的着色、拉姆齐数、距离及控制等内容。本书内容全面，证明与应用实例并举，还给出了证明技巧，书的最后提供了奇数题号的解答或提示。
本书可作为本科生一学期课程教材，也可供图论爱好者自学使用。

1.　Introduction
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
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
3.1.　The Definiition 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
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
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
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
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
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
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
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
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
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

13.　Domination
13.1.　The Domination Number of a Graph  361
13.2.　Exploration:Stratification  372
13.3.　Exploration:Lights Out  377
13.4.　Excursion:And Still It Grows More Colorful  381

Solutions and Hints for Odd-Numbered Exercises  397
References  425
Index of Names  437
Index of Mathematical Terms  440
List of Symbols  447