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Brooks' Theorem

Graph Coloring and Critical Graphs

  • Book
  • © 2024

Overview

Authors:
  1. Michael Stiebitz

    1. Fakultät Mathematik & Naturwissenschaften, Technische Universität Ilmenau, Ilmenau, Germany

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  2. Thomas Schweser

    1. Actian Germany GmbH, Ilmenau, Germany

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  3. Bjarne Toft

    1. Department of Mathematics & Computer Science, The University of Southern Denmark, Odense M, Denmark

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  • A valuable reference to a wealth of information, scattered in journals, proceedings and dissertations
  • Gives easy access to a wealth of information, including best known proofs of the results described
  • Contains excercises and chapter overviews with information on history and further result

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Degree Bounds for the Chromatic Number

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 1-60

  3. Degeneracy and Colorings

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 61-113

  4. Colorings and Orientations of Graphs

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 115-166

  5. Properties of Critical Graphs

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 167-229

  6. Critical Graphs with few Edges

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 231-292

  7. Bounding 𝝌 by 𝚫 and 𝝎

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 293-353

  8. Coloring of Hypergraphs

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 355-400

  9. Homomorphisms and Colorings

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 401-481

  10. Coloring Graphs on Surfaces

    • Michael Stiebitz, Thomas Schweser, Bjarne Toft
    Pages 483-536

  11. Back Matter

    Pages 537-655
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Keywords

About this book

Brooks' Theorem (1941) is one of the most famous and fundamental theorems in graph theory – it is mentioned/treated in all general monographs on graph theory. It has sparked research in several directions. This book presents a comprehensive overview of this development and see it in context. It describes results, both early and recent, and explains relations: the various proofs, the many extensions and similar results for other graph parameters. It serves as a valuable reference to a wealth of information, now scattered in journals, proceedings and dissertations. The reader gets easy access to this wealth of information in comprehensive form, including best known proofs of the results described. Each chapter ends in a note section with historical remarks, comments and further results. The book is also suitable for graduate courses in graph theory and includes exercises. The book is intended for readers wanting to dig deeper into graph coloring theory than what is possible in the existing book literature. There is a comprehensive list of references to original sources.

Authors and Affiliations

  • Fakultät Mathematik & Naturwissenschaften, Technische Universität Ilmenau, Ilmenau, Germany

    Michael Stiebitz

  • Actian Germany GmbH, Ilmenau, Germany

    Thomas Schweser

  • Department of Mathematics & Computer Science, The University of Southern Denmark, Odense M, Denmark

    Bjarne Toft

About the authors

MICHAEL STIEBITZ graduated from Humboldt University in Berlin in 1977. He obtained a doctorate at the Technical University of Ilmenau in 1981 and has served as professor there until 2022. He has published around 70 research papers on graph theory, in particular on coloring problems. He is the main author of the book Graph Edge Coloring (Wiley 2012). 

THOMAS SCHWESER obtained a doctorate at the Technical University of Ilmenau in 2020, supervised by Michael Stiebitz. He has published around 15 research papers and is currently working in the private industrial sector as a researcher in database theory. 


BJARNE TOFT graduated from Aarhus University in 1968 and obtained a doctorate from the University of London in 1970. He is author of around 65 research papers. His mathematical interests are graph theory, combinatorial game theory and the history of mathematics. He co-authored Graph Coloring Problems (Wiley 1995), and is second author of Graph Edge Coloring (Wiley 2012) and HEX The Full Story (CRC Press 2019)

Bibliographic Information

  • Book Title: Brooks' Theorem

  • Book Subtitle: Graph Coloring and Critical Graphs

  • Authors: Michael Stiebitz, Thomas Schweser, Bjarne Toft

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-50065-7

  • Publisher: Springer Cham

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

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024

  • Hardcover ISBN: 978-3-031-50064-0Published: 15 March 2024

  • Softcover ISBN: 978-3-031-50067-1Due: 15 April 2024

  • eBook ISBN: 978-3-031-50065-7Published: 14 March 2024

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XIV, 655

  • Number of Illustrations: 61 b/w illustrations

  • Topics: Graph Theory

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