Computational complexity of the problem of approximation by graphs with connected components of bounded size

New versions of the graph approximation problem with the bounded size of connected components in approximating graphs are proposed. It is shown that if the cardinality of each component in the approximating graphs is less or equal to the given integer $p \geqslant 3$ then the graph approximation problem is $NP$-hard, whereas in the case of $p=2$ the problem is solvable in a polynomial time.