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Princeton University Library Catalog
Elementary Methods of Graph Ramsey Theory [electronic resource] / by Yusheng Li, Qizhong Lin.
1st ed. 2022.
Cham : Springer International Publishing : Imprint: Springer, 2022.
1 online resource (349 pages)
Applied Mathematical Sciences, 211
[More in this series]
Applied Mathematical Sciences, 2196-968X ; 211
[More in this series]
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.
Includes bibliographical references and index.
Small Ramsey Numbers
Basic Probalistic Method
Lovász Local Lemma
Constructive Lower Bounds
Turán Number and Related Ramsey Number
Dependent Random Choice
Regularity Lemma and van der Waerden Number
More Ramsey Linear Functions
Various Ramsey Problems.
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Elementary methods of graph Ramsey theory / Yusheng Li, Qizhong Lin.