  Graph isomorphism, subgraph isomorphism, and maximum common subgraphs are
classical well-investigated objects. Their (parameterized) complexity and
efficiently tractable cases have been studied. In the present paper, for a
given set of forests, we study maximum common induced subforests and minimum
common induced superforests. We show that finding a maximum subforest is
NP-hard already for two subdivided stars while finding a minimum superforest is
tractable for two trees but NP-hard for three trees. For a given set of $k$
trees, we present an efficient greedy
$\left(\frac{k}{2}-\frac{1}{2}+\frac{1}{k}\right)$-approximation algorithm for
the minimum superforest problem. Finally, we present a polynomial time
approximation scheme for the maximum subforest problem for any given set of
forests.
