Contents
1 Introduction
2 What makes a graph dense?
2.1 Thomassen's Conjecture
2.2 Stronger extremal bounds
3 Connections to χ-boundedness
3.1 Esperet's Conjecture
3.2 Minimum degree and clique number
4 Degree-bounding functions
4.1 Dichotomy
4.2 Almost regular graphs
4.3 Unbalanced bipartite graphs
5 Examples
5.1 Convex sets in Euclidean space
5.2 Circle graphs and vertex-minors
5.3 String graphs and induced minors
5.4 Width parameters and a broader trend