03414nam 22006375 450 99649034620331620240221142224.03-031-12762-510.1007/978-3-031-12762-5(MiAaPQ)EBC7088324(Au-PeEL)EBL7088324(CKB)24846072100041(DE-He213)978-3-031-12762-5(PPN)264953908(EXLCZ)992484607210004120220916d2022 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierElementary Methods of Graph Ramsey Theory[electronic resource] /by Yusheng Li, Qizhong Lin1st ed. 2022.Cham :Springer International Publishing :Imprint: Springer,2022.1 online resource (349 pages)Applied Mathematical Sciences,2196-968X ;211Print version: Li, Yusheng Elementary Methods of Graph Ramsey Theory Cham : Springer International Publishing AG,c2022 9783031127618 Includes bibliographical references and index.Existence -- Small Ramsey Numbers -- Basic Probalistic Method -- Random Graph -- Lovász Local Lemma -- Constructive Lower Bounds -- Turán Number and Related Ramsey Number -- Communication Channels -- Dependent Random Choice -- Quasi-Random Graphs -- Regularity Lemma and van der Waerden Number -- More Ramsey Linear Functions -- Various Ramsey Problems.This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner’s overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turán numbers and communication channels, etc.Applied Mathematical Sciences,2196-968X ;211Graph theoryDiscrete mathematicsProbabilitiesGraph TheoryApplications of Discrete MathematicsProbability TheoryTeoria de RamseythubLlibres electrònicsthubGraph theory.Discrete mathematics.Probabilities.Graph Theory.Applications of Discrete Mathematics.Probability Theory.Teoria de Ramsey511.5Li Yusheng1258054Lin QizhongMiAaPQMiAaPQMiAaPQBOOK996490346203316Elementary methods of graph Ramsey theory3008884UNISA