Dynamic monopolies of constant size

Details Dynamic monopolies of constant size Dynamic monopolies of constant size

1999-11-17

arxiv.org/abs/math/9911125v3

Mathematics

Combinatorics

Submitted to Journal of Combinatorial Th. Ser. B. Shared 1st prize at The Technion Excelence Program Conference 1999. 10 pages

Scientific paper

The 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).

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