Ramsey Theory for Discrete Structures

• Main Author: Pr©œmel, Hans J©ơrgen. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Subjects: Mathematics.; Computer science > Mathematics.; Discrete mathematics.; Combinatorics.; Discrete Mathematics.; Discrete Mathematics in Computer Science.
• Online Access: View fulltext via EzAccess

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. ℗ The book first presents a detailed discussion of the roots of Ramsey theory before of...

Table of Contents:

• Foreword by Angelika Steger
• Preface
• Conventions
• Part I Roots of Ramsey Theory: 1.1 RamseyỚ"s theorem
• 1.2 From HilbertỚ"s cube lemma to RadoỚ"s thesis
• Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Definitions and basic examples
• 2.2 Hales-JewettỚ"s theorem
• 2.3 Graham-RothschildỚ"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 Szemer©♭diỚ"s Theorem
• 5.2 Density Hales-Jewett Theorem
• 5.3 Proof of the density Hales-Jewett theorem
• References
• Index.