Friendly bisections of random graphs

We introduce a new method for studying stochastic processes in random graphs controlled by degree information, involving combining enumeration techniques with an abstract second moment argument. We use it to constructively resolve a conjecture of Füredi from 1988: with high probability, the random graph G(n,1/2) admits a friendly bisection of its vertex set, i.e., a partition of its vertex set into two parts whose sizes differ by at most one in which n-o(n) vertices have at least as many neighbours in their own part as across. This work is joint with Asaf Ferber, Matthew Kwan, Bhargav Narayanan, and Mehtaab Sawhney.