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A Kaleidoscopic View of Graph Colorings

  • Book
  • © 2016

Overview

Authors:
  1. Ping Zhang

    1. Dept of Math, Western Michigan Univ, Kalamazoo, USA

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  • Assembles the latest research on chromatic graph theory, vertex colorings, edge colorings, binomial colorings, kaleidoscopic colorings and majestic colorings
  • Contains detailed proofs and illustrations
  • Provides a number of new problems and topics to study?

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (14 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    • Ping Zhang
    Pages 1-6

  3. Binomial Edge Colorings

    • Ping Zhang
    Pages 7-18

  4. Kaleidoscopic Edge Colorings

    • Ping Zhang
    Pages 19-33

  5. Graceful Vertex Colorings

    • Ping Zhang
    Pages 35-51

  6. Harmonious Vertex Colorings

    • Ping Zhang
    Pages 53-61

  7. A Map Coloring Problem

    • Ping Zhang
    Pages 63-66

  8. Set Colorings

    • Ping Zhang
    Pages 67-73

  9. Multiset Colorings

    • Ping Zhang
    Pages 75-83

  10. Metric Colorings

    • Ping Zhang
    Pages 85-94

  11. Sigma Colorings

    • Ping Zhang
    Pages 95-101

  12. Modular Colorings

    • Ping Zhang
    Pages 103-115

  13. A Banquet Seating Problem

    • Ping Zhang
    Pages 117-123

  14. Irregular Colorings

    • Ping Zhang
    Pages 125-135

  15. Recognizable Colorings

    • Ping Zhang
    Pages 137-149

  16. Back Matter

    Pages 151-157
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Keywords

About this book

This book describes kaleidoscopic topics that have developed in the area of graph colorings. Unifying current material on graph coloring, this book describes current information on vertex and edge colorings in graph theory, including harmonious colorings, majestic colorings, kaleidoscopic colorings and binomial colorings.  Recently there have been a number of breakthroughs in vertex colorings that give rise to other colorings in a graph, such as graceful labelings of graphs that have been reconsidered under the language of colorings.

The topics presented in this book include sample detailed proofs and illustrations, which depicts elements that are often overlooked. This book is ideal for graduate students and researchers in graph theory, as it covers a broad range of topics and makes connections between recent developments and well-known areas in graph theory.

Reviews

“This book has the unique goal of covering the non-typical types of colorings in hopes of leading to new research and, in effect, providing a useful text with problems approachable for undergraduate students and up. … The author provides many short proofs that illustrate the different types of proof techniques used to solve these types of graph theory problems. Additionally, the author has included many open questions to show some direction in which to take one's research.” (John Asplund, Mathematical Reviews, November, 2016)

Authors and Affiliations

  • Dept of Math, Western Michigan Univ, Kalamazoo, USA

    Ping Zhang

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