Elementary methods of graph Ramsey theory

by Li, Yusheng

Type Book

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Title Statements

Full title :Elementary methods of graph Ramsey theory / Yusheng Li, Qizhong Lin.

Summary

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 beginners 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.

Edition Statements

Publication Date:2022.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham, Switzerland
Language:eng
Publication Date:2022.

The Physical Object

Description:1 online resource (1 volume) : : illustrations (black and white).

Edition Identifiers

ISBN:9783031127625, 3031127625
DOI:10.1007/978-3-031-12762-5
oclc:on1346157112
LC Classification:QA166
Dewey Decimal:511.5

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.