Elementary Methods of Graph Ramsey Theory

This book provides an overview of elementary methods in graph Ramsey theory, targeted towards graduate students and researchers in extremal graph theory, graph Ramsey theory, and related fields. It is structured in thirteen chapters, with a beginner's overview and application-focused content.

Format: Hardback
Length: 346 pages
Publication date: 17 September 2022
Publisher: Springer International Publishing AG

This comprehensive book is meticulously designed to serve as a valuable resource for graduate students and researchers in the field of graph theory. With a primary focus on extremal graph theory, graph Ramsey theory, and related areas, it offers a comprehensive overview of fundamental methods in the realm of graph Ramsey theory. The text is structured into thirteen chapters, each dedicated to a specific application area while maintaining a high level of independence. This allows readers to selectively delve into topics of interest, tailoring their study to their specific needs.

In the first chapter, a gentle introduction to elementary examples in graph Ramsey theory is provided, primarily utilizing combinatorial methods. This chapter serves as an ideal starting point for those new to the field, providing a solid foundation upon which to build.

The subsequent chapters delve into various topics, including probabilistic methods, algebraic construction, regularity methods, and more. However, this book goes beyond the traditional boundaries of graph Ramsey theory, encompassing a wide range of related and captivating topics. These include the disproof of a conjecture by Borsuk on geometry, intersecting hypergraphs, Turán numbers, and communication channels.

Each chapter is meticulously crafted to provide a clear and concise explanation of the relevant concepts, accompanied by illustrative examples and exercises. The book is well-suited for self-study, serving as a valuable reference for graduate students and researchers seeking to expand their knowledge in graph Ramsey theory and related fields.

Whether you are a seasoned graph theorist or a newcomer to the field, this book will undoubtedly enhance your understanding and appreciation of the complexities of graph Ramsey theory. Its comprehensive coverage, application-focused approach, and wealth of insightful information make it an essential resource for anyone interested in this dynamic and rapidly evolving area of research.

Weight: 705g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031127618
Edition number: 1st ed. 2022