03501nam a22005175i 4500 978-3-031-50065-7 DE-He213 20251030111720.0 cr nn 008mamaa 240314s2024 sz | s |||| 0|eng d 9783031500657 978-3-031-50065-7 10.1007/978-3-031-50065-7 doi QA166-166.247 PBV bicssc MAT008000 bisacsh PBV thema Stiebitz, Michael. author. aut http://id.loc.gov/vocabulary/relators/aut 72998 Brooks' Theorem [electronic resource] : Graph Coloring and Critical Graphs / by Michael Stiebitz, Thomas Schweser, Bjarne Toft. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 655 p. 61 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Monographs in Mathematics, 2196-9922 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 χ by ∆ and ω -- 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. 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. Graph theory. Graph Theory. Schweser, Thomas. author. aut http://id.loc.gov/vocabulary/relators/aut 72999 Toft, Bjarne. author. aut http://id.loc.gov/vocabulary/relators/aut 73000 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031500640 Printed edition: 9783031500664 Printed edition: 9783031500671 Springer Monographs in Mathematics, 2196-9922 73001 https://doi.org/10.1007/978-3-031-50065-7 ZDB-2-SMA ZDB-2-SXMS 58315 58315