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The $(n-\ell)$-deck of an $n$-vertex graph is the multiset of subgraphsobtained from it by deleting $\ell$ vertices. A family of $n$-vertex graphs is$\ell$-recognizable if every graph having the same $(n-\ell)$-deck as a graphin the family is also in the family. We prove that the family of $n$-vertexgraphs with no cycles is $\ell$-recognizable when $n\ge2\ell+1$ (except for$(n,\ell)=(5,2)$). As a consequence, the family of $n$-vertex trees is$\ell$-recognizable when $n\ge2\ell+1$ and $\ell\ne2$. It is known that thisfails when $n=2\ell$.

Acyclic graphs with at least $2\ell+1$ vertices are $\ell$-recognizable