Chromatic graph theory

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
PREFACE TO THE SECOND EDITION
List of Symbols
0: The Origin of Graph Colorings
1: Introduction to Graphs
	1.1 Fundamental Terminology
	1.2 Connected Graphs
	1.3 Distance in Graphs
	1.4 Isomorphic Graphs
	1.5 Common Graphs and Graph Operations
	1.6 Multigraphs and Digraphs
	Exercises for Chapter 1
2: Trees and Connectivity
	2.1 Cut-Vertices, Bridges, and Blocks
	2.2 Trees
	2.3 Connectivity and Edge-Connectivity
	2.4 Menger's Theorem
	Exercises for Chapter 2
3: Eulerian and Hamiltonian Graphs
	3.1 Eulerian Graphs
	3.2 de Bruijn Digraphs
	3.3 Hamiltonian Graphs
	Exercises for Chapter 3
4: Matchings and Factorization
	4.1 Matchings and Independence
	4.2 Factorization and Decomposition
	Exercises for Chapter 4
5: Graph Embeddings
	5.1 Planar Graphs and the Euler Identity
	5.2 Hamiltonian Planar Graphs
	5.3 Planarity versus Nonplanarity
	5.4 Outerplanar Graphs
	5.5 Embedding Graphs on Surfaces
	5.6 The Graph Minor Theorem
	Exercises for Chapter 5
6: Introduction to Vertex Colorings
	6.1 The Chromatic Number of a Graph
	6.2 Applications of Colorings
	6.3 Perfect Graphs
	Exercises for Chapter 6
7: Bounds for the Chromatic Number
	7.1 Color-Critical Graphs
	7.2 Upper Bounds and Greedy Colorings
	7.3 Upper Bounds and Oriented Graphs
	7.4 The Chromatic Number of Cartesian Products
	Exercises for Chapter 7
8: Coloring Graphs on Surfaces
	8.1 The Four Color Problem
	8.2 The Conjectures of Hajós and Hadwiger
	8.3 Chromatic Polynomials
	8.4 The Heawood Map-Coloring Problem
	Exercises for Chapter 8
9: Restricted Vertex Colorings
	9.1 Uniquely Colorable Graphs
	9.2 List Colorings
	9.3 Precoloring Extensions of Graphs
	Exercises for Chapter 9
10: Edge Colorings
	10.1 The Chromatic Index and Vizing's Theorem
	10.2 Class One and Class Two Graphs
	10.3 Tait Colorings
	10.4 Nowhere-Zero Flows
	10.5 List Edge Colorings
	10.6 Total Colorings of Graphs
	Exercises for Chapter 10
11: Ramsey Theory
	11.1 Ramsey Numbers
	11.2 Bipartite Ramsey Numbers
	11.3 s-Bipartite Ramsey Numbers
	Exercises for Chapter 11
12: Monochromatic Ramsey Theory
	12.1 Monochromatic Ramsey Numbers
	12.2 Monochromatic-Bichromatic Ramsey Numbers
	12.3 Proper Ramsey Numbers
	12.4 Rainbow Ramsey Numbers
	12.5 Gallai-Ramsey Numbers
	Exercises for Chapter 12
13: Color Connection
	13.1 Rainbow Connection
	13.2 Proper Connection
	13.3 Rainbow Disconnection
	Exercises for Chapter 13
14: Distance and Colorings
	14.1 T-Colorings
	14.2 L(2; 1)-Colorings
	14.3 Radio Colorings
	14.4 Hamiltonian Colorings
	Exercises for Chapter 14
15: Domination and Colorings
	15.1 Domination Parameters
	15.2 Stratified Domination
	15.3 Domination Based on K3-Colorings
	15.4 Stratified Domination by Multiple Graphs
	Exercises for Chapter 15
16: Induced Colorings
	16.1 Majestic Colorings
	16.2 Royal and Regal Colorings
	16.3 Rainbow Mean Colorings
	Exercises for Chapter 16
17: The Four Color Theorem Revisited
	17.1 Zonal Labelings of Planar Graphs
	17.2 Zonal Labelings and Edge Colorings
	Exercises for Chapter 17
Bibliography
Index (Names and Mathematical Terms)