TY  - BOOK
AU  - Promel, Hans Jurgen.
TI  - Ramsey theory for discrete structures
SN  - 9783319013145 (hard cover : alk. paper)
U1  - 511.6 23
PY  - 2013///
CY  - Switzerland
PB  - Springer
KW  - Ramsey theory.
KW  - Number theory
KW  - Data processing.
KW  -  Computational complexity.
KW  - Combinatorial analysis.
N1  - Includes bibliographical references and index; Part I. Roots of Ramsey Theory --
1. Ramsey's Theorem --
2. From Hilbert's Cube Lemma to Rado's Thesis --

Part II. A Starting Point of Ramsey Theory: Parameter Sets --
3. Definitions and Basic Examples --
4. Hales-Jewett's Theorem --
5. Graham-Rothschild's Theorem --
6. Canonical Partitions --

Part III.  Back to the Roots: Sets --
7. Ramsey Numbers --
8. Rapidly Growing Ramsey Functions --
9. Product Theorems --
10. A Quasi Ramsey Theorem --
11. Partition Relations for Cardinal Numbers --

Part IV. Graphs and Hypergraphs --
12. Finite Graphs --
13. Infinite Graphs --
14. Hypergraphs on Parameter Sets --
15. Ramsey Statements for Random Graphs --
16. Sparse Ramsey Theorems --

Part V. Density Ramsey Theorems --
17. Szemeredi's Theorem --
18. Density Hales-Jewett Theorem--

References--
Index

N2  - This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century
ER  -