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An elementary approach to component sizes in critical random graphs

Part of: Combinatorial probability Graph theory Stochastic processes

Published online by Cambridge University Press:  11 November 2022

Umberto De Ambroggio Open the ORCID record for Umberto De Ambroggio [Opens in a new window]
Umberto De Ambroggio*
Affiliation:
University of Bath
*
*Postal address: Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. Email address: umbidea@gmail.com
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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 a random intersection graph, a random graph obtained through p-bond percolation on a general d-regular graph, and a model of an inhomogeneous random graph.

Keywords

Random walkballot theorem

MSC classification

Primary: 05C80: Random graphs
Secondary: 60G50: Sums of independent random variables; random walks 60C05: Combinatorial probability
Type
Original Article
Information
Journal of Applied Probability , Volume 59 , Issue 4 , December 2022 , pp. 1228 - 1242
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust

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