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Abstract The largest components of the critical Erdős–Rényi graph, G(n, p) with p = 1 / n, have size of order n 2/3 with high probability. We give detailed asymptotics… Click to show full abstract
Abstract The largest components of the critical Erdős–Rényi graph, G(n, p) with p = 1 / n, have size of order n 2/3 with high probability. We give detailed asymptotics for the probability that there is an unusually large component, i.e. of size an 2/3 for large a. Our results, which extend the work of Pittel (2001), allow a to depend upon n and also hold for a range of values of p around 1 / n. We also provide asymptotics for the distribution of the size of the component containing a particular vertex.
Keywords:
probability;
critical erd;
erd nyi;
unusually large;
probability unusually;
nyi graph
Journal Title: Advances in Applied Probability
Year Published: 2017
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Journal Title: Advances in Applied Probability
Year Published: 2017
Link to full text (if available)
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recommendations!