For p = n^{-(e-2)/(3e-2)+ε}, the maximum induced tree size in G(n,p) is concentrated at two adjacent values.
Cliques in random graphs
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Concentration of the maximum size of an induced subtree in moderately sparse random graphs
For p = n^{-(e-2)/(3e-2)+ε}, the maximum induced tree size in G(n,p) is concentrated at two adjacent values.