Abstract
AbstractThe ‐deck of an ‐vertex graph is the multiset of subgraphs obtained from it by deleting vertices. A family of ‐vertex graphs is ‐recognizable if every graph having the same ‐deck as a graph in the family is also in the family. We prove that the family of ‐vertex graphs with no cycles is ‐recognizable when (except for ). As a consequence, the family of ‐vertex trees is ‐recognizable when and . It is known that this fails when .
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