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
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