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.

翻译：图同构、子图同构和最大公共子图是经典的、被广泛研究的对象。它们的（参数化）复杂性及有效可解情况已得到研究。在本文中，针对给定的一组森林，我们研究最大公共诱导子森林和最小公共诱导超森林。我们证明，对于两个细分星形图，寻找最大子森林已是NP难的；而对于两棵树，寻找最小超森林是易解的，但对于三棵树则是NP难的。对于给定的一组$k$棵树，我们为最小超森林问题提出了一种高效的贪婪$\left(\frac{k}{2}-\frac{1}{2}+\frac{1}{k}\right)$-近似算法。最后，我们为任意给定的一组森林的最大子森林问题，提出了一种多项式时间近似方案。