03157nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001800153072001600171072002300187072001500210100008000225245013500305250001800440264006900458300004400527336002600571337002600597338003600623347002400659490005100683505044300734520109101177650001802268650001802286700007902304700007502383710003402458773002602492776003602518776003602554776003602590830005102626856004602677978-3-031-50065-7DE-He21320251030111720.0cr nn 008mamaa240314s2024    sz |    s    |||| 0|eng d  a97830315006577 a10.1007/978-3-031-50065-72doi 4aQA166-166.247 7aPBV2bicssc 7aMAT0080002bisacsh 7aPBV2thema1 aStiebitz, Michael.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aBrooks' Theoremh[electronic resource] :bGraph Coloring and Critical Graphs /cby Michael Stiebitz, Thomas Schweser, Bjarne Toft.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIV, 655 p. 61 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Monographs in Mathematics,x2196-99220 a1 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.  aBrooks' 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. 0aGraph theory.14aGraph Theory.1 aSchweser, Thomas.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aToft, Bjarne.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303150064008iPrinted edition:z978303150066408iPrinted edition:z9783031500671 0aSpringer Monographs in Mathematics,x2196-992240uhttps://doi.org/10.1007/978-3-031-50065-7