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

Author
Li, Yusheng [Browse]
Format
Book
Language
English
Published/​Created
  • Cham : Springer, [2022]
  • ©2022
Description
xiii, 346 pages : illustrations (black and white) ; 25 cm.

Details

Subject(s)
Author
Series
  • Applied mathematical sciences (Springer-Verlag New York Inc.) ; v. 211. [More in this series]
  • Applied mathematical sciences ; Volume 211
Summary note
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.
Bibliographic references
Includes bibliographical references (pages 325-341) and index.
Rights and reproductions note
Current copyright fee: GBP19.00 42\0.
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.
ISBN
  • 3031127617 (hardcover)
  • 9783031127618 (hardcover)
OCLC
1333267335
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