Weakened Ramsey Theory
暫譯: 弱化的拉姆齊理論
Budden, Mark R.
- 出版商: CRC
- 出版日期: 2026-08-13
- 售價: $5,520
- 貴賓價: 9.5 折 $5,244
- 語言: 英文
- 頁數: 170
- 裝訂: Hardcover - also called cloth, retail trade, or trade
- ISBN: 1032807024
- ISBN-13: 9781032807027
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相關分類:
離散數學 Discrete-mathematics
海外代購書籍(需單獨結帳)
商品描述
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.
商品描述(中文翻譯)
《弱化的拉姆齊理論》為讀者提供了有關拉姆齊理論中各種參數的弱化一般化的概述。與其確定一個結構必須多大才能保證在 t-著色中存在單色子結構，弱化的拉姆齊理論則考慮一個結構必須多大才能保證存在一個最多使用給定顏色數的子結構。文獻中已經研究了弱化的拉姆齊數、Gallai-Ramsey 數、Schur 數、Rado 數、彩虹 Schur 數等的弱化一般化，本書提供了已知結果的全面概述，並附有完整的證明。
本書應該對高年級本科生、研究生以及從事拉姆齊理論研究的研究人員提供有價值的資源。僅假設讀者具備圖論、代數和數論的基本背景，並包含重要定義和背景結果的簡明回顧。
特色
- 自成體系的主題處理，只需具備圖論、代數和數論的最小背景
- 弱化拉姆齊理論主要結果的完整證明
- 大量彩色圖形以協助讀者
- 全面的參考文獻列表
- 拉姆齊理論中已知弱化參數的表格，為研究人員提供有用的參考。
作者簡介
Mark Rowland Budden completed his Ph.D. in Mathematics in 2003 at the University of Missouri-Columbia. He was a faculty member at Armstrong Atlantic State University (now Georgia Southern University's Armstrong campus) until 2010, when he joined the faculty at Western Carolina University, where he is now a professor. He has published 47 research articles and is the author of the book Star-Critical Ramsey Numbers for Graphs. Most of his research is in Ramsey theory or other related topics in combinatorial number theory, and the majority of his publications have included student coauthors.
作者簡介(中文翻譯)
馬克·羅蘭·巴登於2003年在密蘇里大學哥倫比亞分校獲得數學博士學位。他曾是阿姆斯特朗大西洋州立大學（現為喬治亞南方大學的阿姆斯特朗校區）的教職員，直到2010年加入西卡羅來納大學的教職，現在擔任教授。他已發表47篇研究文章，並著有書籍《圖的星臨界拉姆齊數》。他的研究大多集中在拉姆齊理論或其他相關的組合數論主題，且大部分出版物均有學生共同作者。
