作者：B.Bollobas
页数：412
出版社：世界图书出版公司
出版日期：2003
ISBN：9787506259637
电子书格式：PDF
PDF下载地址
内容简介
本书包含图论的经典理论和很多近代研究成果，也探讨了图论与其它数学分支的重要联系。全书共10章: 基础；电网络；流、连通和匹配；极值图论；染色；Ramsey理论；随机图论；图、群和矩阵；图和群、图和矩阵；图上的随机道路；Tatte多项式。
读者对象：相关专业的研究生及研究人员。
作者简介
孟菲斯大学（University of Memphis）数学系教授。著有 Extremal Graph Theory ，Graph Theory: An Introductory Course，Modern Graph Theory等多部研究生教材。
目录
Apologia
Preface
Ⅰ Fundamentals
Ⅰ.1 Definitions
Ⅰ.2 Paths, Cycles, and Trees
Ⅰ.3 Hamilton Cycles and Euler Circuits
Ⅰ.4 Planar Graphs
Ⅰ.5 An Application of Euler Trails to Algebra
Ⅰ.6 Exercises
Ⅱ Electrical Networks
Ⅱ.1 Graphs and Electrical Networks
Ⅱ.2 Squaring the Square
Ⅱ.3 Vector Spaces and Matrices Associated with Graphs
Ⅱ.4 Exercises
Ⅱ.5 Notes
Ⅲ Flows, ConnectⅣity and Matching
Ⅲ.1 Flows in Directed Graphs
Ⅲ.2 ConnectⅣity and Menger’s Theorem
Ⅲ.3 Matching
Ⅲ.4 Tutte’s 1-Factor Theorem
Ⅲ.5 Stable Matchings
Ⅲ.6 Exercises
Ⅲ.7 Notes
Ⅳ Extremal Problems
Ⅳ.1 Paths and Cycles
Ⅳ.2 Complete Subgraphs
Ⅳ.3 Hamilton Paths and Cycles
Ⅳ.4 The Structure of Graphs
Ⅳ.5 Szemeredi’s Regularity Lemma
Ⅳ.6 Simple Applications of Szemer&ti’s Lernma
Ⅳ.7 Exercises
Ⅳ.8 Notes
Ⅴ Colouring
Ⅴ.1 Vertex Colouring
Ⅴ.2 Edge Colouring
Ⅴ.3 Graphs on Surfaces
Ⅴ.4 List Colouring
Ⅴ.5 Perfect Graphs
Ⅴ.6 Exercises
Ⅴ.7 Notes
Ⅵ Ramsey Theory
Ⅵ.1 The Fundamental Rarnsey Theorems
Ⅵ.2 Canonical Ramsey Theorems
Ⅵ.3 Ramsey Theory For Graphs
Ⅵ.4 Ramsey Theory for Integers
Ⅵ.5 Subsequances
Ⅵ.6 Exercises
Ⅵ.7 Notes
Ⅶ Random Graphs
Ⅶ.1 The Basic Models—The Use of the Expectation
Ⅶ.2 Simple Properties of Almost All Graphs
Ⅶ.3 Almost Determined VariableskThe Use of the Variance
Ⅶ.4 Hamilton Cycles—The Use of Graph Theoretic Tools.
Ⅶ.5 The Phase Transition
Ⅶ.6 Exercises
Ⅶ.7 Notes
Ⅷ Graphs, Groups and Matrices
Ⅷ.1 Cayley and Schreier Diagrams
Ⅷ.2 The Adjacency Matrix and the Laplacian
Ⅷ.3 Strongly Regular Graphs
Ⅷ.4 Enumeration and P61ya’s Theorem
Ⅷ.5 Exercises
Ⅸ Random Walks on Graphs
Ⅸ.1 Electrical Networks Revisited
Ⅸ.2 Electrical Networks and Random Walks
Ⅸ.3 Hitting Times and Commute Times
Ⅸ.4 Conductance and Rapid Mixing
Ⅸ.5 Exercises
Ⅸ.6 Notes
Ⅹ The TaRe Polynomial
Ⅹ.1 Basic Properties of the Tutte Polynomial
Ⅹ.2 The UnⅣersal Form of the Tutte Polynomial
Ⅹ.3 The Tutte Polynomial in Statistical Mechanics
Ⅹ.4 Special Values of the “luRe Polynomial
Ⅹ.5 A Spanning Tree Expansion of the Tutte Polynomial
Ⅹ.6 Polynomials of Knots and Links
Ⅹ.7 Exercises
Ⅹ.8 Notes
Symbol Index
Name Index
Subject Index
Preface
Ⅰ Fundamentals
Ⅰ.1 Definitions
Ⅰ.2 Paths, Cycles, and Trees
Ⅰ.3 Hamilton Cycles and Euler Circuits
Ⅰ.4 Planar Graphs
Ⅰ.5 An Application of Euler Trails to Algebra
Ⅰ.6 Exercises
Ⅱ Electrical Networks
Ⅱ.1 Graphs and Electrical Networks
Ⅱ.2 Squaring the Square
Ⅱ.3 Vector Spaces and Matrices Associated with Graphs
Ⅱ.4 Exercises
Ⅱ.5 Notes
Ⅲ Flows, ConnectⅣity and Matching
Ⅲ.1 Flows in Directed Graphs
Ⅲ.2 ConnectⅣity and Menger’s Theorem
Ⅲ.3 Matching
Ⅲ.4 Tutte’s 1-Factor Theorem
Ⅲ.5 Stable Matchings
Ⅲ.6 Exercises
Ⅲ.7 Notes
Ⅳ Extremal Problems
Ⅳ.1 Paths and Cycles
Ⅳ.2 Complete Subgraphs
Ⅳ.3 Hamilton Paths and Cycles
Ⅳ.4 The Structure of Graphs
Ⅳ.5 Szemeredi’s Regularity Lemma
Ⅳ.6 Simple Applications of Szemer&ti’s Lernma
Ⅳ.7 Exercises
Ⅳ.8 Notes
Ⅴ Colouring
Ⅴ.1 Vertex Colouring
Ⅴ.2 Edge Colouring
Ⅴ.3 Graphs on Surfaces
Ⅴ.4 List Colouring
Ⅴ.5 Perfect Graphs
Ⅴ.6 Exercises
Ⅴ.7 Notes
Ⅵ Ramsey Theory
Ⅵ.1 The Fundamental Rarnsey Theorems
Ⅵ.2 Canonical Ramsey Theorems
Ⅵ.3 Ramsey Theory For Graphs
Ⅵ.4 Ramsey Theory for Integers
Ⅵ.5 Subsequances
Ⅵ.6 Exercises
Ⅵ.7 Notes
Ⅶ Random Graphs
Ⅶ.1 The Basic Models—The Use of the Expectation
Ⅶ.2 Simple Properties of Almost All Graphs
Ⅶ.3 Almost Determined VariableskThe Use of the Variance
Ⅶ.4 Hamilton Cycles—The Use of Graph Theoretic Tools.
Ⅶ.5 The Phase Transition
Ⅶ.6 Exercises
Ⅶ.7 Notes
Ⅷ Graphs, Groups and Matrices
Ⅷ.1 Cayley and Schreier Diagrams
Ⅷ.2 The Adjacency Matrix and the Laplacian
Ⅷ.3 Strongly Regular Graphs
Ⅷ.4 Enumeration and P61ya’s Theorem
Ⅷ.5 Exercises
Ⅸ Random Walks on Graphs
Ⅸ.1 Electrical Networks Revisited
Ⅸ.2 Electrical Networks and Random Walks
Ⅸ.3 Hitting Times and Commute Times
Ⅸ.4 Conductance and Rapid Mixing
Ⅸ.5 Exercises
Ⅸ.6 Notes
Ⅹ The TaRe Polynomial
Ⅹ.1 Basic Properties of the Tutte Polynomial
Ⅹ.2 The UnⅣersal Form of the Tutte Polynomial
Ⅹ.3 The Tutte Polynomial in Statistical Mechanics
Ⅹ.4 Special Values of the “luRe Polynomial
Ⅹ.5 A Spanning Tree Expansion of the Tutte Polynomial
Ⅹ.6 Polynomials of Knots and Links
Ⅹ.7 Exercises
Ⅹ.8 Notes
Symbol Index
Name Index
Subject Index