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 -bond percolation on a general -regular graph, and a model of inhomogeneous random graph.
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