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Color-Induced Graph Colorings

  • Book
  • © 2015

Overview

Authors:
  1. Ping Zhang

    1. Department of Mathematics, Western Michigan University, Kalamazoo, USA

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  • Provides intriguing open problems and conjectures
  • Offers a comprehensive treatment of numerous color-induced graph colorings
  • Presents the background and motivation for the concept of color-induced colorings of graphs
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Ping Zhang
    Pages 1-4

  3. The Irregularity Strength of a Graph

    • Ping Zhang
    Pages 5-29

  4. Modular Sum-Defined Irregular Colorings

    • Ping Zhang
    Pages 31-42

  5. Set-Defined Irregular Colorings

    • Ping Zhang
    Pages 43-50

  6. Multiset-Defined Irregular Colorings

    • Ping Zhang
    Pages 51-60

  7. Sum-Defined Neighbor-Distinguishing Colorings

    • Ping Zhang
    Pages 61-68

  8. Modular Sum-Defined Neighbor-Distinguishing Colorings

    • Ping Zhang
    Pages 69-79

  9. Strong Edge Colorings of Graphs

    • Ping Zhang
    Pages 81-94

  10. Sum-Defined Chromatic Indices

    • Ping Zhang
    Pages 95-111

  11. Back Matter

    Pages 113-118
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Keywords

About this book

A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings as well as researchers and graduate students in the mathematics community, especially the graph theory community.

Reviews

“The book gives a detailed survey on concepts of vertex-colorings which are induced by edge-colorings. … It is well written and provides a good introduction and survey on color-induced graph colorings for researchers and graduate students in the mathematics community, especially the graph theory community.” (Eckhard Steffen, zbMATH, Vol. 1365.05006, 2017)

Authors and Affiliations

  • Department of Mathematics, Western Michigan University, Kalamazoo, USA

    Ping Zhang

Bibliographic Information

  • Book Title: Color-Induced Graph Colorings

  • Authors: Ping Zhang

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-20394-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Ping Zhang 2015

  • Softcover ISBN: 978-3-319-20393-5Published: 18 August 2015

  • eBook ISBN: 978-3-319-20394-2Published: 10 August 2015

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XIV, 118

  • Number of Illustrations: 48 b/w illustrations

  • Topics: Graph Theory, Combinatorics

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