# Large-scale structures in random graphs

## TL;DR

This paper surveys recent advances in understanding large substructures in random graphs, focusing on thresholds, robustness, and new methods like sparse regularity, absorbing, and container techniques.

## Contribution

It highlights the development of new methods in graph theory for analyzing large structures in random graphs and discusses open problems in the field.

## Key findings

- Progress in threshold determination for substructure appearance
- Development of new methods like sparse regularity and absorbing techniques
- Identification of open questions in large-scale random graph structures

## Abstract

In recent years there has been much progress in graph theory on questions of the following type. What is the threshold for a certain large substructure to appear in a random graph? When does a random graph contain all structures from a given family? And when does it contain them so robustly that even an adversary who is allowed to perturb the graph cannot destroy all of them? I will survey this progress, and highlight the vital role played by some newly developed methods, such as the sparse regularity method, the absorbing method, and the container method. I will also mention many open questions that remain in this area.