Weakened Ramsey Theory (Discrete Mathematics and Its Applications)

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. FeaturesSelf-contained treatment of