Chromatic Graph Theory: 1st Edition (Hardback) book cover

Chromatic Graph Theory

1st Edition

By Gary Chartrand, Ping Zhang

Chapman and Hall/CRC

504 pages | 278 B/W Illus.

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pub: 2008-09-22
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Description

Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics.

This self-contained book first presents 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. The remainder of the text deals exclusively with graph colorings. It 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, and many distance-related vertex colorings.

With historical, applied, and algorithmic discussions, this text offers a solid introduction to one of the most popular areas of graph theory.

Reviews

… The book is written in a student-friendly style with carefully explained proofs and examples and contains many exercises of varying difficulty. … The book is intended for standard courses in graph theory, reading courses and seminars on graph colourings, and as a reference book for individuals interested in graphs colourings.

Zentralblatt MATH 1169

… well-conceived and well-written book … written in a reader-friendly style, and there is a sufficient number of exercises at the end of each chapter.

—Miklós Bóna, University of Florida, MAA Online, January 2009

Table of Contents

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

Trees

Connectivity and Edge-Connectivity

Menger’s Theorem

Eulerian and Hamiltonian Graphs

Eulerian Graphs

de Bruijn Digraphs

Hamiltonian Graphs

Matchings and Factorization

Matchings

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

T-Colorings

L(2, 1)-Colorings

Radio Colorings

Hamiltonian Colorings

Domination and Colorings

Epilogue

Appendix: Study Projects

General References

Bibliography

Index (Names and Mathematical Terms)

List of Symbols

Exercises appear at the end of each chapter.

About the Series

Discrete Mathematics and Its Applications

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
COM046000
COMPUTERS / Operating Systems / General
COM051300
COMPUTERS / Programming / Algorithms
MAT036000
MATHEMATICS / Combinatorics