Resolution of a conjecture on majority dynamics: rapid stabilisation in dense random graphs

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Colleges, School and Institutes

External organisations

  • University of New South Wales (UNSW) Australia
  • Graz Tech Univ


We study majority dynamics on the binomial random graph G(n,p) with p = d/n and d > c n^{1/2}, for some large c>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.


Original languageEnglish
JournalRandom Structures and Algorithms
Publication statusPublished - 10 Jul 2020


  • majority dynamics, random graphs, unanimity

ASJC Scopus subject areas