2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79423The paper deals with a polling game on a graph. Initially, each vertex is colored white or black. At each round, each vertex is colored by the color shared by the majority of vertices in its neighborhood. We say that a set of vertices is a dynamic monopoly if starting the game with the vertices of the set colored white, the entire system is white after a finite number of rounds. Peleg asked how small a dynamic monopoly may be as a function of the number of vertices. We show that the answer is O(1).Submitted to Journal of Combinatorial Th. Ser. B. Shared 1st prize at The Technion Excelence Program Conference 1999. 10 pages. three figures. v1 and v3 differ only by representationCombinatoricstext