Chromatic Graph Theory / Gary Chartrand.

Features of the Second Edition:

The book can be used for a first course in graph theory as well as a graduate course
The primary topic in the book is graph coloring
The book begins with an introduction to graph theory so assumes no previous course
The authors are the most widely-published team on graph theory
Many new examples and exercises enhance the new edition

Chapter Chapter 0: The Origin of Graph Colorings
Chapter Chapter 1: Introduction to Graphs
Chapter Chapter 2: Trees and Connectivity
Chapter Chapter 3: Eulerian and Hamiltonian Graphs
Chapter Chapter 4: Matchings and Factorization
Chapter Chapter 5: Graph Embeddings
Chapter Chapter 6: Introduction to Vertex Colorings
Chapter Chapter 7: Bounds for the Chromatic Number
Chapter Chapter 8: Coloring Graphs on Surfaces
Chapter Chapter 9: Restricted Vertex Colorings
Chapter Chapter 10: Edge Colorings
Chapter Chapter 11: Ramsey Theory
Chapter Chapter 12: Monochromatic Ramsey Theory
Chapter Chapter 13: Color Connection
Chapter Chapter 14: Distance and Colorings
Chapter Chapter 15: Domination and Colorings
Chapter Chapter 16: Induced Colorings
Chapter Chapter 17: The Four Color Theorem Revisited

With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings.