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Chromatic Graph Theory

Chromatic Graph Theory by Gary Chartrand
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The Origin of Graph Colorings

Introduction to Graphs
Fundamental Terminology
Connected Graphs
Distance in Graphs
Isomorphic Graphs
Common Graphs and Graph Operations
Multigraphs and Digraphs

Trees and Connectivity
Cut Vertices, Bridges, and Blocks
Connectivity and Edge-Connectivity
Menger’s Theorem

Eulerian and Hamiltonian Graphs
Eulerian Graphs
de Bruijn Digraphs
Hamiltonian Graphs

Matchings and Factorization
Independence in Graphs
Factors and Factorization

Graph Embeddings
Planar Graphs and the Euler Identity
Hamiltonian Planar Graphs
Planarity versus Nonplanarity
Embedding Graphs on Surfaces
The Graph Minor Theorem

Introduction to Vertex Colorings
The Chromatic Number of a Graph
Applications of Colorings
Perfect Graphs

Bounds for the Chromatic Number
Color-Critical Graphs
Upper Bounds and Greedy Colorings
Upper Bounds and Oriented Graphs
The Chromatic Number of Cartesian Products

Coloring Graphs on Surfaces
The Four Color Problem
The Conjectures of Hajós and Hadwiger
Chromatic Polynomials
The Heawood Map-Coloring Problem

Restricted Vertex Colorings
Uniquely Colorable Graphs
List Colorings
Precoloring Extensions of Graphs

Edge Colorings of Graphs
The Chromatic Index and Vizing’s Theorem
Class One and Class Two Graphs
Tait Colorings
Nowhere-Zero Flows
List Edge Colorings
Total Colorings of Graphs

Monochromatic and Rainbow Colorings
Ramsey Numbers
Turán’s Theorem
Rainbow Ramsey Numbers
Rainbow Numbers of Graphs
Rainbow-Connected Graphs
The Road Coloring Problem

Complete Colorings
The Achromatic Number of a Graph
Graph Homomorphisms
The Grundy Number of a Graph

Distinguishing Colorings
Edge-Distinguishing Vertex Colorings
Vertex-Distinguishing Edge Colorings
Vertex-Distinguishing Vertex Colorings
Neighbor-Distinguishing Edge Colorings

Colorings, Distance, and Domination
L(2, 1)-Colorings
Radio Colorings
Hamiltonian Colorings
Domination and Colorings

Appendix: Study Projects

General References


Index (Names and Mathematical Terms)

List of Symbols

Exercises appear at the end of each chapter.

CRC Press; September 2008
499 pages; ISBN 9781584888017
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Title: Chromatic Graph Theory
Author: Gary Chartrand; Ping Zhang
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