Weakened Ramsey Theory

Weakened Ramsey Theory provides readers with an overview of weakened generalizations of various parameters studied in Ramsey theory. Rather than determining how large a structure must be to guarantee the existence of monochromatic substructures in a t-coloring, weakened Ramsey theory considers how large a structure must be to guarantee the existence of a substructure that uses at most a given number of colors. Weakened generalizations of Ramsey numbers, Gallai-Ramsey numbers, Schur numbers, Rado numbers, rainbow Schur numbers, and others have all been studied in the literature, and this book offers a thorough overview of the known results, with complete proofs.

This book should prove a valuable resource to advanced undergraduates, graduate students, and researchers working in Ramsey theory. Only a basic background in graph theory, algebra, and number theory is assumed, although a concise review of important definitions and background results is included.

Features

• Self-contained treatment of the subject, requiring only a minimal background in graph theory, algebra, and number theory
• Complete proofs of major results in weakened Ramsey theory
• Numerous color figures to assist the reader
• Comprehensive list of references
• Tables of known weakened parameters in Ramsey theory, providing a useful reference for researchers.