We study majority dynamics on the binomial random graph $G(n,p)$ with $p = d/n$ and $d > \lambda n^{ 1/2}$, for some large $\lambda>0$. In this process, each vertex has a state in $\{ -1,+1 \}$ and at each round every vertex adopts the state of the majority of its neighbours, retaining its state in the case of a tie. We show that with high probability the process reaches unanimity in at most four rounds. This confirms a conjecture of Benjamini, Chan, O' Donnel, Tamuz and Tan.
Categories: math.CO math.PR