498 Pages 278 B/W Illustrations
    by Chapman & Hall

    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.

    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.


    Biography

    Gary Chartrand, Ping Zhang

    … 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