Recent progress in graph theory using expansion

Abstract

Graph expansion has long been recognised as an important and desirable property with applications in a wide range of areas in computer science and mathematics. A particular form of expansion known as `sublinear expansion' has recently been used particularly effectively in extremal graph theory, leading to the resolution of many long-standing and notable problems over the last decade and an improved understanding of the structure of sparse graphs. This survey will cover these advances.

21 pages, survey for the ICM