Brooks' Theorem

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.

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

Auteur

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)

Résumé

"There are multiple problems in each chapter, copious notes on the results and a substantial bibliography. It seems likely this book will be a valuable resource for results and methods in this area for a long time." (David B. Penman, zbMATH 1536.05004, 2024)

Contenu
1 Degree Bounds for the Chromatic Number.- 2 Degeneracy and Colorings.- 3 Colorings and Orientations of Graphs.- 4 Properties of Critical Graphs.- 5 Critical Graphs with few Edges.- 6 Bounding by and .- 7 Coloring of Hypergraphs.- 8 Homomorphisms and Colorings.- 9 Coloring Graphs on Surface.- Appendix A: Brooks' Fundamental Paper.- Appendix B: Tutte's Lecture from 1992.- Appendix C: Basic Graph Theory Concepts.