English

An elementary approach to component sizes in critical random graphs

Probability 2022-02-01 v2 Combinatorics

Abstract

In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models of random graphs when considered at criticality. Specifically, we apply our method to a model of random intersection graph, a random graph obtained through pp-bond percolation on a general dd-regular graph, and a model of inhomogeneous random graph.

Keywords

Cite

@article{arxiv.2101.06625,
  title  = {An elementary approach to component sizes in critical random graphs},
  author = {Umberto De Ambroggio},
  journal= {arXiv preprint arXiv:2101.06625},
  year   = {2022}
}

Comments

16 pages - minor revision. A very similar version accepted by Journal of Applied Probability

R2 v1 2026-06-23T22:14:23.089Z