A Kaleidoscopic View of Graph Colorings

1. Front Matter

   Pages i-xiii

   PDF

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

    PDF

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.

• chromatic graph theory
• chromatic index
• chromatic number
• edge coloring
• graph theory
• vertex coloring
• Kaleidoscopic View
• Graph Colorings
• Four Color Problem
• binomial colorings
• kaleidoscopic colorings
• majestic colorings
• region colorings of planar graphs
• Complete Kaleidoscopes
• Eulerian Graphs and Digraphs
• Strong Edge Colorings
• Graceful Labelings
• Harmonious Colorings
• Harmonious Labelings
• Banquet Seating Problem

“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)

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

  Ping Zhang

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