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Topics in Gallai-Ramsey Theory

  • Book
  • © 2020

Overview

Authors:
  1. Colton Magnant

    1. Advanced Analytics Group, United Parcel Service, Atlanta, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Pouria Salehi Nowbandegani

    1. Department of Mathematics, Vanderbilt University, Nashville, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Explores Gallai-Ramsey Theory
  • Contains strategies and technique to obtain fundamental results
  • Features complete proofs, open problems, and detailed illustrations

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-viii
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  2. Introduction and Basic Definitions

    • Colton Magnant, Pouria Salehi Nowbandegani
    Pages 1-7

  3. General Structure Under Forbidden Rainbow Subgraphs

    • Colton Magnant, Pouria Salehi Nowbandegani
    Pages 9-23

  4. Gallai-Ramsey Results for Rainbow Triangles

    • Colton Magnant, Pouria Salehi Nowbandegani
    Pages 25-79

  5. Gallai-Ramsey Results for Other Rainbow Subgraphs

    • Colton Magnant, Pouria Salehi Nowbandegani
    Pages 81-96

  6. Conclusion and Open Problems

    • Colton Magnant, Pouria Salehi Nowbandegani
    Pages 97-102

  7. Back Matter

    Pages 103-104
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Keywords

About this book

This book explores topics in Gallai-Ramsey theory, which looks into whether rainbow colored subgraphs or monochromatic subgraphs exist in a sufficiently large edge-colored complete graphs. A comprehensive survey of all known results with complete references is provided for common proof methods. Fundamental definitions and preliminary results with illustrations guide readers to comprehend recent innovations. Complete proofs and influential results are discussed with numerous open problems and conjectures. Researchers and students with an interest in edge-coloring, Ramsey Theory, and colored subgraphs will find this book a valuable guide for entering Gallai-Ramsey Theory.

Reviews

“In the opinion of the reviewer, Topics in Gallai-Ramsey theory is a well-organized, well-written, valuable compendium of results in the foundation and halfway up to the second story of the newly christened area of Gallai-Ramsey theory. … this book and efforts in the area will have helped to shape whatever comes next.” (Peter D. Johnson, Jr., Mathematical Reviews, April, 2022)

“This book is an excellent and much sought after material addressing Gallai-Ramsey theory. … this book is meant for very serious researchers in this topic.” (V. Yegnanarayanan, zbMATH 1452.05001, 2021)

Authors and Affiliations

  • Advanced Analytics Group, United Parcel Service, Atlanta, USA

    Colton Magnant

  • Department of Mathematics, Vanderbilt University, Nashville, USA

    Pouria Salehi Nowbandegani

Bibliographic Information

  • Book Title: Topics in Gallai-Ramsey Theory

  • Authors: Colton Magnant, Pouria Salehi Nowbandegani

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-48897-0

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2020

  • Softcover ISBN: 978-3-030-48896-3Published: 05 July 2020

  • eBook ISBN: 978-3-030-48897-0Published: 04 July 2020

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: VIII, 104

  • Number of Illustrations: 67 b/w illustrations

  • Topics: Graph Theory, Combinatorics

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