Ramsey Theory for Discrete Structures

Part I. Roots of Ramsey Theory

1. Ramsey’s Theorem
Hans Jürgen Prömel

2. From Hilbert’s Cube Lemma to Rado’s Thesis
Hans Jürgen Prömel

Part II. A Starting Point of Ramsey Theory: Parameter Sets

3. Definitions and Basic Examples
Hans Jürgen Prömel

4. Hales-Jewett’s Theorem
Hans Jürgen Prömel

5. Graham-Rothschild’s Theorem
Hans Jürgen Prömel

6. Canonical Partitions
Hans Jürgen Prömel

Part III. Back to the Roots: Sets

7. Ramsey Numbers
Hans Jürgen Prömel

8. Rapidly Growing Ramsey Functions
Hans Jürgen Prömel

9. Product Theorems
Hans Jürgen Prömel

10. A Quasi Ramsey Theorem
Hans Jürgen Prömel

11. Partition Relations for Cardinal Numbers
Hans Jürgen Prömel

Part IV. Graphs and Hypergraphs

12. Finite Graphs
Hans Jürgen Prömel

13. Infinite Graphs
Hans Jürgen Prömel

14. Hypergraphs on Parameter Sets
Hans Jürgen Prömel

15. Ramsey Statements for Random Graphs
Hans Jürgen Prömel

16. Sparse Ramsey Theorems
Hans Jürgen Prömel

Part V. Density Ramsey Theorems

17. Szemerédi’s Theorem
Hans Jürgen Prömel

18. Density Hales-Jewett Theorem
Hans Jürgen Prömel

Nyckelord: Mathematics, Combinatorics, Discrete Mathematics, Discrete Mathematics in Computer Science