Graph Theory and Additive Combinatorics: Exploring Structure and Randomness

ISBN-13: 9781009310949 / Twarda / 2023 / 338 str.

Yufei (Massachusetts Institute of Technology) Zhao

Opis

An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.

Recenzje

'This is a wonderful, well-written account of additive combinatorics from the graph theoretic perspective. Zhao skillfully ties in this approach to the usual statements and gives a thorough development of the subject. This book is indispensable for any serious researcher in this area. Beginners will find a thorough account of the subject with plenty of motivation. The more experienced reader will appreciate the authors' insights and elegant development of some difficult ideas.' Andrew Granville, University of Montréal

Spis treści

Preface; Notation and Conventions; Appetizer: triangles and equations; 1. Forbidding a subgraph; 2. Graph regularity method; 3. Pseudorandom graphs; 4. Graph limits; 5. Graph homomorphism inequalities; 6. Forbidding 3-term arithmetic progressions; 7. Structure of set addition; 8. Sum-product problem; 9. Progressions in sparse pseudorandom sets; References; Index.