Chapter 1 Acyclic Coloring
1.1 Basic Definitions and Notations
1.2 Acyclic Vertex Coloring
1.3 Generalized Acyclic Vertex Coloring
1.3.1 r-acyclic Vertex Coloring
1.3.2 Degenerating Coloring
1.4 Acyclic Edge Coloring
1.5 Open Problems
Reference
Chapter 2 Neighbor Sum Distinguishing Coloring
2.1 Basic Definitions and Introduction
2.2 Neighbor Sum Distinguishing Edge Coloring of Graphs
2.2.1 The Conjecture and Related Results
2.2.2 The List Version of Neighbor Sum Distinguishing Edge Colorings
2.3 Neighbor Sum Distinguishing Total Coloring of Graphs
2.3.1 The Conjecture and Related Results
2.3.2 Neighbor Sum Distinguishing Total Choosability of Graphs
2.4 Equitable Neighbor Sum Distinguishing Coloring
Reference
Chapter 3 Edge Cover Coloring
3.1 The Edge Cover Coloring of Graphs
3.1.1 Edge Cover Chromatic Index and Classi-cation of Graphs
3.1.2 Edge Covered Critical Graphs
3.1.3 Unsolved Problems on Edge Cover Coloring
3.2 Fractional Edge Cover Coloring of Graphs
3.2.1 Introduction
3.2.2 Main Results on Fractional Edge Cover Coloring of Graphs
3.2.3 The Conjectures and Discussions on Fractional Edge Cover Coloring
3.3 g-edge Cover Coloring of Graphs
3.3.1 g-edge Cover Chromatic Index of Graphs
3.3.2 g-Edge Covered Critical Graphs
3.3.3 Related Problems on g-edge Cover Coloring of Graphs
Reference
Chapter 4 f-colorings of Graphs
4.1 Introduction
4.2 Basic Definitions and Tools
4.3 f-colorings of Multigraphs
4.4 The Classification Problem of Simple Graphs on f-Colorings
4.4.1 Main Results
4.4.2 Application in Proper Edge Colorings of Simple Graphs
4.4.3 Further Discussion
4.5 Critical Graphs on f-colorings
4.5.1 Some Properties of f-critical Graphs
4.5.2 Bounds on the Number of Edges of f-critical Graphs
4.5.3 f-regular f-critical Graphs
4.5.4 f-critical Graphs with The f-core Having Maximum Degree
4.5.5 Some problems for future research
4.6 Equitable Edge-colorings of Simple Graphs
4.6.1 A Useful Lemma
4.6.2 A Problem for Further Research
Reference
Chapter 5 Total Coloring
5.1 Introduction
5.2 Total Coloring Conjecture and the Related Results on △≥9
5.2.1 Total Coloring Conjecture
5.3 Total Coloring of Graph G with △(G)≤8
5.3.1 The Results on the Case △≤8
5.3.2 The Results on the Case △≤7
5.4 List Total Coloring of Graphs
5.5 The Open Problems and Conjectures
Reference
Index

蔡建生、王纪辉、张霞著的《图的有限制条件染色引论(英文版)》旨在作为这一项引人入胜和活跃领域的最新推测、结果和相关方法的集合体，可以作为参考手册或参考。
作者不想涵盖各种限制性的图形着色，一个明显的原因是这个分支发展得太快，作者无法将所有的主题都包含在其中，另一个重要的原因是一些早期的书中已经涵盖了一些结果和猜想。在本书中，作者主要关注的是理论这一分支中的所有方面，不包括由于空间限制而产生的算法方面，而且作者只强调新的结果和新的方法。