Chromatic Thresholds and Related Problems

In this series of lectures, we will go over the classical chromatic threshold problems in extremal graph theory. At its core, this type of problems seeks for sufficient density conditions for graphs with forbidden substructure to have bounded complexity (in this particular case, bounded chromatic number). After covering the basics and classical results, we will then introduce some recent developments which connects this area to other areas such as combinatorial convexity, VC dimension theory, additive combinatorics etc.

Prerequisite: basic knowledge of graph theory.

1. Turan problem and stability.
2. When does dense triangle-free graph have bounded chromatic number?
3. Connections to VC dimension theory.
4. Beyond chromatic threshold.
5. Chromatic thresholds for linear equations.