# Reduction for the Maximum Subforest Problem

I'm trying to find (without luck) the reduction for the Maximum Subforest Problem.

INSTANCE: Tree $G=\left(V,E\right)$ and a set of trees H.

SOLUTION: A subset $E'\subseteq E$ such that the subgraph $G'=\left(V,E'\right)$ does not contain any subtree isomorphic to a tree from H. MEASURE: Cardinality of the subgraph, i.e., $\vert E'\vert$.

Any idea on where I can find a paper or solution for this problem?

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I don't know. The only reference I found is Ron Shamir and Dekel Tsur, The maximum subforest problem: approximation and exact algorithms (extended abstract), Proceedings of the Ninth Annual ACM-SIAM Symposium on Discrete Algorithms (San Francisco, CA, 1998), 394–399, ACM, New York, 1998. There is also a discussion of maximal subforests in Chapter 2 of Part C of Lucchesi et al, Aspectos teóricos da computaç ao, Projeto Euclides, 8, Instituto de Matemática Pura e Aplicada, Rio de Janeiro, 1979, but it's in Portugese. –  Gerry Myerson Jun 29 '11 at 1:31