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2016 On the largest component in the subcritical regime of the Bohman-Frieze process
Sanchayan Sen
Electron. Commun. Probab. 21: 1-15 (2016). DOI: 10.1214/16-ECP20

Abstract

Kang, Perkins, and Spencer [7] conjectured that the size of the largest component of the Bohman-Frieze process at a fixed time $t$ smaller than $t_c$, the critical time for the process, is $L_1(t)=O(\log n/(t_c-t)^2)$ with high probability. Bhamidi, Budhiraja, and Wang [3] have shown that a bound of the form $L_1(t_n)=O((\log n)^4/(t_c-t_n)^2)$ holds with high probability for $t_n\leq t_c-n^{-\gamma }$ where $\gamma \in (0,1/4)$. In this paper, we improve the result in [3] by showing that for any fixed $\lambda >0$, $L_1(t_n)=O(\log n/(t_c-t_n)^2)$ with high probability for $t_n\leq t_c-\lambda n^{-1/3}$. In particular, this settles the conjecture in [7].

Citation

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Sanchayan Sen. "On the largest component in the subcritical regime of the Bohman-Frieze process." Electron. Commun. Probab. 21 1 - 15, 2016. https://doi.org/10.1214/16-ECP20

Information

Received: 4 May 2016; Accepted: 30 August 2016; Published: 2016
First available in Project Euclid: 14 September 2016

zbMATH: 1346.60006
MathSciNet: MR3548776
Digital Object Identifier: 10.1214/16-ECP20

Subjects:
Primary: 05C80, 60C05

JOURNAL ARTICLE
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