Ramsey Theory for Discrete Structures

Foreword by Angelika Steger.- Preface.- Conventions.- Part I Roots of Ramsey Theory: 1.1 Ramsey's theorem.- 1.2 From Hilbert's cube lemma to Rado's thesis.- Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Definitions and basic examples.- 2.2 Hales-Jewett's theorem.- 2.3 Graham-Rothschild's theorem.- 2.4 Canonical partitions.- Part III Back to the Roots: Sets: 3.1 Ramsey numbers.- 3.2 Rapidly growing Ramsey functions.- 3.3 Product theorems.- 3.4 A quasi Ramsey theorem.- 3.5 Partition relations for cardinal numbers.- Part IV Graphs and Hypergraphs: 4.1 Finite graphs.- 4.2 Infinite graphs.- 4.3 Hypergraphs on parameter sets.- 4.4. Ramsey statements for random graphs.- 4.5 Sparse Ramsey Theorems.- Part V Density Ramsey Theorems: 5.1 Szemerédi's Theorem.- 5.2 Density Hales-Jewett Theorem.- 5.3 Proof of the density Hales-Jewett theorem.- References.- Index.