图论导引
出版信息
[美] Douglas B.West / 机械工业出版社 / 2004-10 / 59.00元
内容简介
图论在计算科学、社会科学和自然科学等各个领域都有广泛应用。本书是本科生或研究生一学期或两学期的图论课程教材。全书力求保持按证明的难度和算法的复杂性循序渐进的风格，使学生能够深入理解书中的内容。书中包括对证明技巧的讨论、1200多道习题、400多幅插图以及许多例题，而且对所有定理都给出了详细完整的证明。虽然本书包括许多算法和应用，但是重点在于理解图论结构和分析图论问题的技巧。
目录
Preface
Chapter 1 Fundamental Concepts
1.1 What Is a Graph?
The Definition
Graphs as Models
Matrices and Ismorphism
Decomposition and Special Graphs
Exercises
1.2 Paths,Cycles,and Trails
Connection in Graphs
Bipartite Graphs
Exercises
1.3 Vertex Degrees and Counting
Counting and Bijections
Extremal Problems
Graphic Sequences
Excercises
1.4 Directed Graphs
Definitions and Examples
Vertex Degrees
Eulerian Digraphs
Orientations and Tournaments
Exercises
Chapter 2 Trees and Distance
2.1 Basic Properties
Properties of Trees
Distance in Trees and Graphs
Disjoint Spanning Trees(optional)
Exercises
2.2 Spanning Trees and Enumeration
Enumeration of Trees
Spanning Trees in Graphs
Decomposition and Graceful Labelings
Branchings and Eulerian Digraphs(optional)
2.3 Optimization and Trees
Minimum Spanning Tree
Shortese Paths
Trees in Computer Science(optional)
Exercises
Chapter 3 Matchings and Factors
3.1 Matchings and Covers
Maximum Matchings
Hall's Matching Condition
Min-Max Theorems
Independent Sets and Covers
Dominating Sets(optional)
Exercises
3.2 Algorithms and Applications
Maximum Bipartite Matching
Weighted Bipartite Matching
Stable Matchings(optional)
Faster Bipartite Matching(optional)
Exercises
3.3 Matchings in General Graphs
Tutt's 1-factor Hteorem
f-factors of Graphs(optional)
Edmonds'Blossom Algorithm(optional)
Exercises
……
