The Power of Small Coalitions in Graphs
نویسندگان
چکیده
This paper considers the question of the in uence of a coalition of vertices seeking to gain control or majority in local neighborhoods in a general graph Say that a vertex v is controlled by the coalition M if the majority of its neighbors are fromM We ask how many vertices as a function of jM j can M control in this fashion Upper and lower bounds are provided for this problem as well as for cases where the majority is computed over larger neighborhoods either neighborhoods of some xed radius r or all neighborhoods of radii up to r In particular we look also at the case where the coalition must control all vertices outside itself and derive bounds for its size I S CNRS Universite de Nice Sophia Antipolis Bat ESSI Route des Colles BP F Sophia Antipolis France E mail bermond diamant unice fr Department of Applied Mathematics and Computer Science The Weizmann Institute Rehovot Israel E mail peleg wisdom weizmann ac il
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