Large-scale structures in random graphs
Combinatorics
2017-02-10 v1
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.
Cite
@article{arxiv.1702.02648,
title = {Large-scale structures in random graphs},
author = {Julia Böttcher},
journal= {arXiv preprint arXiv:1702.02648},
year = {2017}
}
Comments
55 pages, Survey for 26th BCC