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

The $(n-ell)$-deck of an $n$-vertex graph is the multiset of subgraphs obtained 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 graph in the family is also in the family. We prove that the family of $n$-vertex graphs having no cycles is $ell$-recognizable when $nge2ell+1$ (except for $(n,ell)=(5,2)$). It is known that this fails when $n=2ell$.