A Simple Branching Process Approach to the Phase Transition in $G_{n,p}$

Béla Bollobás, Oliver Riordan

Abstract


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 $(np-1)^3n\to\infty$.


Keywords


random graph; phase transition; branching process

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