Elementary Methods of Graph Ramsey Theory

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Exercises included

Readers can easily extract basic idea underlying each approach

Written for graduate students in graph theory

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2022
Fachbereich:	Allgemeines
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Applied Mathematical Sciences
Inhalt:	xiii 346 S. 10 s/w Illustr. 346 p. 10 illus.
ISBN-13:	9783031127618
ISBN-10:	3031127617
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Lin, Qizhong Li, Yusheng
Auflage:	1st ed. 2022
Hersteller:	Springer International Publishing Springer International Publishing AG Applied Mathematical Sciences
Maße:	241 x 160 x 25 mm
Von/Mit:	Qizhong Lin (u. a.)
Erscheinungsdatum:	17.09.2022
Gewicht:	0,705 kg