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- W1903001324 abstract "Kang, Perkins and Spencer showed 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 $L_1(t)=Omega(log n/(t_c-t)^2)$ with high probability. They also conjectured that this is the correct order, that is $L_1(t)=O(log n/(t_c-t)^2)$ with high probability for fixed $t$ smaller than $t_c$. Using a different approach, Bhamidi, Budhiraja and Wang showed that $L_1(t_n)=O((log n)^4/(t_c-t_n)^2)$ with high probability for $t_nleq t_c-n^{-gamma}$ where $gammain(0,1/4)$. In this paper, we improve their result by showing that for any fixed $lambda>0$, $L_1(t_n)=O(log n/(t_c-t_n)^2)$ with high probability for $t_nleq t_c-lambda n^{-1/3}$. In particular, this settles the conjecture of Kang, Perkins and Spencer. We also prove some generalizations for general bounded size rules." @default.
- W1903001324 created "2016-06-24" @default.
- W1903001324 creator A5002978817 @default.
- W1903001324 date "2013-07-08" @default.
- W1903001324 modified "2023-10-03" @default.
- W1903001324 title "On the largest component in the subcritical regime of the Bohman-Frieze process" @default.
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- W1903001324 doi "https://doi.org/10.48550/arxiv.1307.2041" @default.
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