Items related to Ramsey Theory: Unsolved Problems and Results
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
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About the Author
Xiaodong Xu and Haipeng Luo, Guangxi Academy of Science, China; Meilian Liang, Guangxi University, China
"About this title" may belong to another edition of this title.
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Xiaodong Xu and Haipeng Luo, Guangxi Academy of Science, China Meilian Liang, Guangxi University, China Key problems and conjectures have played an important role in promoting the development of Ramsey theory. Seller Inventory # 237726565
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - 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 Erdös-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 190 pp. Englisch. Seller Inventory # 9783110576511
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