  A bipartite graph $G=(L,R;E)$ with at least one edge is said to be
identifiable if for every vertex $v\in L$, the subgraph induced by its
non-neighbors has a matching of cardinality $|L|-1$. An $\ell$-subgraph of $G$
is an induced subgraph of $G$ obtained by deleting from it some vertices in $L$
together with all their neighbors. The Identifiable Subgraph problem is the
problem of determining whether a given bipartite graph contains an identifiable
$\ell$-subgraph.
  We show that the Identifiable Subgraph problem is polynomially solvable,
along with the version of the problem in which the task is to delete as few
vertices from $L$ as possible together with all their neighbors so that the
resulting $\ell$-subgraph is identifiable. We also complement a known
APX-hardness result for the complementary problem in which the task is to
minimize the number of remaining vertices in $L$, by showing that two
parameterized variants of the problem are W[1]-hard.
