A simple branching process approach to the phase transition in Gn,p
It is well known that the branching process approach to the study of the random graph Gn,p gives a very simple way of understanding the size of the giant component when it is fairly large (of order Θ(n)). Here we show that a variant of this approach works all the way down to the phase transition: we use branching process arguments to give a simple new derivation of the asymptotic size of the largest component whenever.
Electronic Journal of Combinatorics
Bollobás, B., & Riordan, O. (2012). A simple branching process approach to the phase transition in Gn,p. Electronic Journal of Combinatorics, 19 (4) https://doi.org/10.37236/2588