Ramsey Theory

Xiaodong Xu

ISBN 10: 3110576511 / ISBN 13: 9783110576511

Edité par De Gruyter, Mercury Learning And Information Aug 2018, 2018

A propos de cet article

This item is printed on demand - Print on Demand Titel. Neuware -Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms.ContentsSome definitions and notationsRamsey theoryBi-color diagonal classical Ramsey numbersPaley graphs and lower bounds for R(k, k)Bi-color off-diagonal classical Ramsey numbersMulticolor classical Ramsey numbersGeneralized Ramsey numbersFolkman numbersThe Erd¿s¿Hajnal conjectureOther Ramsey-type problems in graph theoryOn van der Waerden numbers and Szemeredi¿s theoremMore problems of Ramsey type in additive number theorySidon¿Ramsey numbersGames in Ramsey theoryLocal Ramsey theorySet-coloring Ramsey theoryOther problems and conjecturesWalter de Gruyter GmbH, Genthiner Strasse 13, 10785 Berlin 190 pp. Englisch.

N° de réf. du vendeur 9783110576511

Détails bibliographiques

• Titre: Ramsey Theory
• Éditeur: De Gruyter, Mercury Learning And Information Aug 2018
• Date de parution: 2018
• Langue: anglais
• ISBN à 10 chiffres: 3110576511
• ISBN à 13 chiffres: 9783110576511
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 246 L x 175 H x 16 P (en millimètres) 246 millimètres de largeur par 175 millimètres de hauteur par 16 millimètres de profondeur
• Poids: 511 grammes

A propos de ce titre

Synopsis

Key problems and conjectures have played an important role in promoting the development of Ramsey theory, a field where great progress has been made during the past two decades, with some old problems solved and many new problems proposed. The present book will be helpful to readers who wish to learn about interesting problems in Ramsey theory, to see how they are interconnected, and then to study them in depth. This book is the first problem book of such scope in Ramsey theory. Many unsolved problems, conjectures and related partial results in Ramsey theory are presented, in areas such as extremal graph theory, additive number theory, discrete geometry, functional analysis, algorithm design, and in other areas. Most presented problems are easy to understand, but they may be difficult to solve. They can be appreciated on many levels and by a wide readership, ranging from undergraduate students majoring in mathematics to research mathematicians. This collection is an essential reference for mathematicians working in combinatorics and number theory, as well as for computer scientists studying algorithms.

Contents
Some definitions and notations
Ramsey theory
Bi-color diagonal classical Ramsey numbers
Paley graphs and lower bounds for R(k, k)
Bi-color off-diagonal classical Ramsey numbers
Multicolor classical Ramsey numbers
Generalized Ramsey numbers
Folkman numbers
The Erdős-Hajnal conjecture
Other Ramsey-type problems in graph theory
On van der Waerden numbers and Szemeredi's theorem
More problems of Ramsey type in additive number theory
Sidon-Ramsey numbers
Games in Ramsey theory
Local Ramsey theory
Set-coloring Ramsey theory

Other problems and conjectures

À propos de l?auteur

Xiaodong Xu and Haipeng Luo, Guangxi Academy of Science, China; Meilian Liang, Guangxi University, China