Ramsey Theory

Unsolved Problems and Results

Xiaodong Xu, Meilian Liang, Haipeng Luo , University of Science & Technology

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English

De Gruyter
06 August 2018

Algebra; Number theory; Combinatorics & graph theory

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

By: Xiaodong Xu, Meilian Liang, Haipeng Luo
Contributions by: University of Science & Technology
Imprint: De Gruyter
Country of Publication: Germany
Dimensions: Height: 240mm, Width: 170mm, Spine: 13mm
Weight: 450g
ISBN: 9783110576511
ISBN 10: 3110576511
Pages: 190
Publication Date: 06 August 2018
Audience: Professional and scholarly , Undergraduate , Undergraduate
Format: Hardback
Publisher's Status: Active

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