English

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.

Keywords

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

R2 v1 2026-06-22T18:13:22.140Z