Bowler–Brown–Fenner tree-recognition conjecture

Let $G$ be a graph on $n$ vertices, and let a card be an unlabeled vertex-deleted subgraph $G-v$. Bowler–Brown–Fenner conjecture. For $n\geq 44$, it can be determined whether $G$ is a tree from any $\lfloor\frac{n}{2}\rfloor+2$ of its cards. The conjecture gives the expected sharp number of cards needed to recognize trees from incomplete decks; the source does not state whether it has been resolved.