In this paper we study variants of well-known graph problems as vertex cover, spanning tree, matchings, and hamiltonian path. Given a graph G = (V, E), we add a partition Π V (resp. Π E) of its vertices (resp. of its edges). Now, any solution S containing an element (vertex or edge) of a part of this partition must also contain all the others ones. In other words, elements can only be added set by set, instead of one by one as in the classical situation. We propose hardness and approximation results.