Graph Theory and Additive Combinatorics: Exploring Structure and Randomness

This book provides a modern introduction to extremal graph theory and additive combinatorics, exploring central results through graph theoretic perspectives and highlighting important methods. It is intended for students and researchers in combinatorics, theoretical computer science, analysis, probability, and number theory.

Format: Hardback
Length: 338 pages
Publication date: 31 July 2023
Publisher: Cambridge University Press

This comprehensive text delves into the realm of extremal graph theory and additive combinatorics, employing the dichotomy of structure and pseudorandomness as a central theme. It offers a modern introduction to these subjects, making them accessible to readers with a basic understanding of abstract algebra, analysis, and linear algebra.

The book begins by exploring fundamental concepts in additive combinatorics, including the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao. Through graph theoretic perspectives, readers gain deeper insights into these ideas, while also exploring topics such as the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem.

Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted throughout the text, providing students with a solid foundation for further study in these fields. Chapter summaries, numerous figures, and exercises aid in comprehension, while freely available lecture videos on MIT OpenCourseWare further enhance the learning experience.

Designed as an introduction for students and researchers pursuing combinatorics, theoretical computer science, analysis, probability, and number theory, this text assumes only a basic familiarity with abstract algebra, analysis, and linear algebra. It serves as a valuable resource for those seeking to delve into the world of extremal graph theory and additive combinatorics.

Weight: 766g
Dimension: 183 x 260 x 24 (mm)
ISBN-13: 9781009310949