The coalition structure generation (CSG) problem consists in partitioning a group of agents into coalitions to maximize the sum of their values. We consider here the case of coalitional games whose characteristic function is compactly represented by a set of weighted conjunctive formulae (an MC-net). In this context the CSG problem is known to be computationally hard in general. In this paper, we first study some key parameters of MC-nets that complicate solving the CSG problem. Then we consider a specific class of MC-nets, called bipolar MC-nets, and prove that the CSG problem is polynomial for this class. Finally, we show that the CS-core of a game represented by a bipolar MC-net is never empty, and that an imputation belonging to the CS-core can be computed in polynomial time.