在Erdős-Rényi随机图上有明显的k4渗透阈值

IF 1.1 3区数学 Q2 STATISTICS & PROBABILITY

Electronic Journal of Probability Pub Date : 2022-01-01 DOI:10.1214/21-ejp710

Brett Kolesnik

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引用次数: 4

摘要

我们找到了临界阈值pc ~ 1/√3n logn，在此阈值下，通过迭代完成K4减去一条边的副本，可以从Erdős-Rényi图Gn,p中获得完整图Kn。这改进了Balogh, Bollobás和Morris的工作，将阈值限定为乘法常数。

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The sharp K4-percolation threshold on the Erdős–Rényi random graph

We locate the critical threshold pc ∼ 1/ √ 3n logn at which it becomes likely that the complete graph Kn can be obtained from the Erdős–Rényi graph Gn,p by iteratively completing copies of K4 minus an edge. This refines work of Balogh, Bollobás and Morris that bounds the threshold up to multiplicative constants.

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来源期刊

Electronic Journal of Probability 数学-统计学与概率论

CiteScore

1.80

自引率

7.10%

发文量

119

审稿时长

4-8 weeks

期刊介绍： The Electronic Journal of Probability publishes full-size research articles in probability theory. The Electronic Communications in Probability (ECP), a sister journal of EJP, publishes short notes and research announcements in probability theory. Both ECP and EJP are official journals of the Institute of Mathematical Statistics and the Bernoulli society.