Weakened Ramsey Theory
Series: Discrete Mathematics and Its Applications;
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Product details:
- Edition number 1
- Publisher Chapman and Hall
- Date of Publication 14 August 2026
- ISBN 9781032807027
- Binding Hardback
- No. of pages190 pages
- Size 254x178 mm
- Language English
- Illustrations 86 Illustrations, color; 86 Line drawings, color; 9 Tables, black & white 700
Categories
Short description:
Weakened Ramsey Theory provides readers with an overview of weakened generalizations of various parameters studied in Ramsey theory. It is a valuable resource for advanced undergraduates, graduate students, and researchers working in Ramsey theory.
MoreLong description:
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.
Table of Contents:
1. Foundations in Ramsey Theory 2. Chromatic Ramsey Numbers 3. Weakened Ramsey Numbers 4. Weakened Ramsey Theory on the Integers 5. Going Forward
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