Elementary methods of graph Ramsey theory / Yusheng Li, Qizhong Lin.

Format:

Book

Author/Creator:

Li, Yusheng (Writer on mathematics), author.

Lin, Qizhong, author.

Series:

Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 211.

Applied mathematical sciences, 0066-5452 ; Volume 211

Language:

English

Subjects (All):

Ramsey theory.

Physical Description:

xiii, 346 pages : illustrations (black and white) ; 25 cm.

Place of Publication:

Cham : Springer, [2022]

Summary:

This book in 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 studens 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.--back cover.

Contents:

1. Existence

2. Small Ramsey numbers

3. Basic probabilistic method

4. Random graph

5. Lovász local lemma

6. Constructive lower bounds

7. Turán number and related Ramsey number

8. Communication channels

9. Dependent random choice

10. Quasi-random graphs

11. Regularity lemma and van der Waerden number

12. More Ramsey linear functions

13. Various Ramsey problems

References

Glossary

Index.

Notes:

Includes bibliographical references (pages 325-341) and index.

Current copyright fee: GBP19.00 42\0.

ISBN:

3031127617

9783031127618

OCLC:

1333267335