It is well known that the branching process approach to the study of the random graph $G_{n,p}$ gives a very simple way of understanding the size of the giant component when it is fairly large (of order $\Theta(n)$). 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 $(np-1)^3n\to\infty$.
@article{10_37236_2588,
author = {B\'ela Bollob\'as and Oliver Riordan},
title = {A simple branching process approach to the phase transition in {\(G_{n,p}\)}},
journal = {The electronic journal of combinatorics},
year = {2012},
volume = {19},
number = {4},
doi = {10.37236/2588},
zbl = {1266.05149},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2588/}
}
TY - JOUR
AU - Béla Bollobás
AU - Oliver Riordan
TI - A simple branching process approach to the phase transition in \(G_{n,p}\)
JO - The electronic journal of combinatorics
PY - 2012
VL - 19
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/2588/
DO - 10.37236/2588
ID - 10_37236_2588
ER -
%0 Journal Article
%A Béla Bollobás
%A Oliver Riordan
%T A simple branching process approach to the phase transition in \(G_{n,p}\)
%J The electronic journal of combinatorics
%D 2012
%V 19
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/2588/
%R 10.37236/2588
%F 10_37236_2588
Béla Bollobás; Oliver Riordan. A simple branching process approach to the phase transition in \(G_{n,p}\). The electronic journal of combinatorics, Tome 19 (2012) no. 4. doi: 10.37236/2588
