Ramsey Theory : Unsolved Problems and Results / Xiaodong Xu, Meilian Liang, Haipeng Luo.

Format:

Book

Author/Creator:

Xu, Xiaodong (Professor of Chinese art), author.

Liang, Meilian, author.

Luo, Haipeng, author.

Contributor:

University of Science & Technology.

Language:

English

Subjects (All):

Ramsey theory.

Combinatorial analysis.

Graph theory.

Physical Description:

1 online resource (190 pages)

Place of Publication:

Berlin ; Boston : De Gruyter, [2018]

Language Note:

In English.

Summary:

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 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

Contents:

Frontmatter

Preface / Xu, Xiaodong

Contents

1. Some Definitions And Notations

2. Ramsey Theory

3. Bi-Color Diagonal Classical Ramsey Numbers

4. Paley Graphs And Lower Bounds For R(K, K)

5. Bi-Color Off-Diagonal Classical Ramsey Numbers

6. Multicolor Classical Ramsey Numbers

7. Generalized Ramsey Numbers

8. Folkman Numbers

9. The Erdős-Hajnal Conjecture

10. Other Ramsey-Type Problems In Graph Theory

11. On Van Der Waerden Numbers And Szemerédi'S Theorem

12. More Problems Of Ramsey Type In Additive Number Theory

13. Sidon-Ramsey Numbers

14. Games In Ramsey Theory

15. Local Ramsey Theory

16. Set-Coloring Ramsey Theory

17. Other Problems And Conjectures

Epilogue

Bibliography

Index

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 26. Mrz 2019)

ISBN:

9783110576634

3110576635

9783110576702

3110576708

OCLC:

1048948547