Abstract Problems like the directed feedback vertex set problem have much better algorithms in tournaments when compared to general graphs. This motivates us to study a natural generalization of tournaments, named c -tournaments, and see if the structural properties of these graphs are helpful in obtaining similar algorithms. c -tournaments are simple digraphs which have directed paths of length at most c ≥ 1 between all pairs of vertices. We study the complexity of feedback vertex set and r -dominating set in c -tournaments. We also present hardness results on some graph editing problems involving c -tournaments.