Elementary methods of graph Ramsey theory
著者
書誌事項
Elementary methods of graph Ramsey theory
（Applied mathematical sciences, v. 211）
Springer, c2022
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注記
Includes bibliographical references (p. 325-341) and index
内容説明・目次
内容説明
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, Turan numbers and communication channels, etc.
目次
Existence.- Small Ramsey Numbers.- Basic Probalistic Method.- Random Graph.- Lovasz Local Lemma.- Constructive Lower Bounds.- Turan 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.
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