  We prove that every point-determining digraph $D$ contains a vertex $v$ such
that $D-v$ is also point determining. We apply this result to show that for any
$\{0,1\}$-matrix $M$, with $k$ diagonal zeros and $\ell$ diagonal ones, the
size of a minimal $M$-obstruction is at most $(k+1)(\ell+1)$. This extends the
results of Sumner, and of Feder and Hell, from undirected graphs and symmetric
matrices to digraphs and general matrices.
