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Abstract

Resolving a conjecture of Füredi from 1988, we prove that 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 more neighbours in their own part as across. Our proof is constructive, and in the process, we develop a new method to study stochastic processes driven by degree information in random graphs; this involves combining enumeration techniques with an abstract second moment argument.