Forming k coalitions and facilitating relationships in social networks.

In this paper we relax two common assumptions that are made when studying coalition formation. The first is that any number of coalitions can be formed; the second is that any possible coalition can be formed. We study a model of coalition formation where the value depends on a social network and exactly k coalitions must be formed. Additionally, in this context we present a new problem for an organizer that would like to introduce members of the social network to each other in order to increase the social welfare or to stabilize a coalition structure.