Rudiments of Ramsey Theory: Second Edition
About this Title
Ron Graham, University of California, San Diego, La Jolla, CA and Steve Butler, Iowa State University, Ames, IA
Publication: CBMS Regional Conference Series in Mathematics
Publication Year 2015: Volume 123
ISBNs: 978-0-8218-4156-3 (print); 978-1-4704-2667-5 (online)
MathSciNet review: MR3409216
MSC: Primary 05D10; Secondary 05-02, 05C55
In every sufficiently large structure which has been partitioned there will always be some well-behaved structure in one of the parts. This takes many forms. For example, colorings of the integers by finitely many colors must have long monochromatic arithmetic progressions (van der Waerden's theorem); and colorings of the edges of large graphs must have monochromatic subgraphs of a specified type (Ramsey's theorem). This book explores many of the basic results and variations of this theory.
Since the first edition of this book there have been many advances in this field. In the second edition the authors update the exposition to reflect the current state of the art. They also include many pointers to modern results.
Graduate students and researchers interested in combinatorics, in particular, Ramsey theory.
Table of Contents
- Chapter 1. Three views of Ramsey theory
- Chapter 2. Ramsey’s theorem
- Chapter 3. van der Waerden’s theorem
- Chapter 4. The Hales-Jewett theorem
- Chapter 5. Szemerédi’s theorem
- Chapter 6. Graph Ramsey theory
- Chapter 7. Euclidean Ramsey theory
- Chapter 8. A general Ramsey product theorem
- Chapter 9. The theorems of Schur, Folkman, and Hindman
- Chapter 10. Rado’s theorem
- Chapter 11. Current trends