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Full Description
Weakened Ramsey Theory provides readers with an overview of weakened generalizations of various parameters studied in Ramsey theory. Rather that 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 are 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.
Contents
1. Foundations in Ramsey Theory 2. Chromatic Ramsey Numbers 3. Weakened Ramsey Numbers 4. Weakened Ramsey Theory on the Integers 5. Going Forward
