經典原版書庫·圖論導引

基本介紹

內容簡介

圖論在計算科學、社會科學和自然科學等各個領域都有廣泛套用。本書是本科生
或研究生一學期或兩學期的圖論課程教材。全書力求保持按證明的難度和算法的複雜
性循序漸進的風格，使學生能夠深入理解書中的內容。書中包括對證明技巧的討論、
1200多道習題、400多幅插圖以及許多例題，而且對所有定理都給出了詳細完整的證明
。雖然本書包括許多算法和套用，但是重點在於理解圖論結構和分析圖論問題的技巧
。

作者簡介

作者：(美國)韋斯特

圖書目錄

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
……

經典原版書庫·圖論導引

基本介紹

基本介紹

內容簡介

作者簡介

圖書目錄

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