Friendly bisections of random graphs

Resolving a conjecture of Füredi from 1988, we prove that with high probability, the random graph G ( n , 1 / 2 stretchy="false">) \mathbb {G}(n,1/2) admits friendly bisection its vertex set, i.e., partition set into two parts whose sizes differ by at most one in which alttext="n minus o − o encoding="application/x-tex">n-o(n) vertices have more neighbours their own part as across. Our proof is constructive, and process, develop new method to study stochastic processes driven degree information graphs; this involves combining enumeration techniques an abstract second moment argument.