Dynamic monopolies of constant size
Combinatorics
2007-05-23 v3
Abstract
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).
Keywords
Cite
@article{arxiv.math/9911125,
title = {Dynamic monopolies of constant size},
author = {Eli Berger},
journal= {arXiv preprint arXiv:math/9911125},
year = {2007}
}
Comments
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 representation