We establish NP-completeness of two problems on core stable coalitions in hedonic games. In the first problem every player has only two acceptable coalitions in his preference list, and in the second problem the preference structures arise from the distances in an underlying metric space.
Deineko, V. G., & Woeginger, G. J. (2013). Two hardness results for core stability in hedonic coalition formation games. Discrete Applied Mathematics, 161(13-14), 1837-1842. https://doi.org/10.1016/j.dam.2013.03.003