图论导引

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
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