  A classical vertex Ramsey result due to Ne\v{s}et\v{r}il and R\"odl states
that given a finite family of graphs $\mathcal{F}$, a graph $A$ and a positive
integer $r$, if every graph $B\in\mathcal{F}$ has a $2$-vertex-connected
subgraph which is not a subgraph of $A$, then there exists an
$\mathcal{F}$-free graph which is vertex $r$-Ramsey with respect to $A$. We
prove that this sufficient condition for the existence of an $\mathcal{F}$-free
graph which is vertex $r$-Ramsey with respect to $A$ is also necessary for
large enough number of colours $r$.
  We further show a generalisation of the result to a family of graphs and the
typical existence of such a subgraph in a dense binomial random graph.
