出版社:科学出版社
年代:2011
定价:66.0
图论在20世纪得到了飞速的发展,其中一个主要的原因是其在物理学、化学、社会学及计算机科学等领域应用广泛。本书主要介绍了图论中一些基础课题的背景知识。包括K连通图的Dirac定理,线图的Harary-Nashwilliam定理,欧拉图的Toida-McKee公理,图的Tutte矩阵,平面图的Kuratowski定理的傅里叶证明方法等。
Preface
Ⅰ Basic Results
1.0 Introduction
1.1 Basic Concepts
1.2 Subgraphs
1.3 Degrees of Vertices
1.4 Paths and Connectedness
1.5 Automorphism of a Simple Graph
1.6 Line Graphs
1.7 Operations on Graphs
1.8 An Application to Chemistry
1.9 Miscellaneous Exercises
Notes
Ⅱ Directed Graphs
2.0 Introduction
2.1 Basic Concepts
2.2 Tournaments
2.3 k—Partite Tournaments
Notes
Ⅲ Connectivity
3.0 Introduction
3.1 Vertex Cuts and Edge Cuts
3.2 Connectivity and Edge—Connectivity
3.3 Blocks
3.4 Cyclical Edge—Connectivity of a Graph
3.5 Menger's Theorem
3.6 Exercises
Notes
Ⅳ Trees
4.0 Introduction
4.1 Definition, Characterization, and Simple Properties
4.2 Centers and Centroids
4.3 Counting the Number of Spanning Trees
4.4 Cayley's Formula
4.5 Helly Property
4.6 Exercises
Notes
Ⅴ Independent Sets and Matchings
5.0 Introduction
5.1 Vertex Independent Sets and Vertex Coverings
5.2 Edge—lndependent Sets
5.3 Matchings and Factors
5.4 Matchings in Bipartite Graphs
5.5* Perfect Matchings and the Tutte Matrix
Notes
Ⅵ Eulerian and Hamiltonian Graphs
6.0 Introduction
6.1 Eulerian Graphs
6.2 Hamiltonian Graphs
6.3* Pancyclic Graphs
6.4 Hamilton Cycles in Line Graphs
6.52—Factorable Graphs
6.6 Exercises
Notes
Ⅶ Graph Colorings
7.0 Introduction
7.1 Vertex Colorings
7.2 Critical Graphs
7.3 Triangle—Free Graphs
7.4 Edge Colorings of Graphs
7.5 Snarks
7.6 Kirkman's Schoolgirls Problem
7.7 Chromatic Polynomials
Notes
Ⅷ Planarity
8.0 Introduction
8.1 Planar and Nonplanar Graphs
8.2 Euler Formula and Its Consequences
8.3 K5 and K3,3 are Nonplanar Graphs
8.4 Dual of a Plane Graph
8.5 The Four—Color Theorem and the Heawood Five—Color Theorem
8.6 Kuratowski's Theorem
8.7 Hamiltonian Plane Graphs
8.8 Talt Coloring
Notes
Ⅸ Triangulated Graphs
9.0 Introduction
9.1 Perfect Graphs
9.2 Triangulated Graphs
9.3 Interval Graphs
9.4 Bipartite Graph B(G) of a Graph G
9.5 Circular Arc Graphs
9.6 Exercises
9.7 Phasing of Traffic Lights at a Road Junction
Notes
Ⅹ Applications
10.0 Introduction
10.1 The Connector Problem
10.2 Kruskal's Algorithm
10.3 Prim's Algorithm
10.4 Shortest—Path Problems
10.5 Timetable Problem
10.6 Application to Social Psychology
10.7 Exercises
Notes
List of Symbols
References
Index
《图论教程(影印版)》作者是印度巴拉克里什南(BalakrishnanR.)。《图论教程(影印版)》是“国外数学名著系列”丛书中的一本。《图论教程(影印版)》关键词:图论、教材、英文。《图论教程(影印版)》由北京京华虎彩印刷有限公司印刷。《图论教程(影印版)》由各地新华书店经销。
徐俊明, 著
(德) 迪斯特尔 (Diestel) , 著
(加) 塔特 (Tutte,W.T.) , 著
(美) 巴克利 (Buckley,F.) , (美) 勒文特 (Lewinter,M.) , 著
(美) 查特朗, 张萍, 著
(美) 韦斯特 (West,D.B.) , 著
(英) 比格斯 (Biggs,N.) , 著
(美) 威尔逊 (Wilson,R.J.) , 编著
(英) 威尔逊 (Wilson,R.J.) , 著