Solution (source code)

= Solution

\b[False.] Use only the directed <edge> $u\to v$, but choose $v$ first in the outer loop of <depth-first search>. It finishes before a second discovery tree starts at $u$: $d[v]=1$, $f[v]=2$, $d[u]=3$, $f[u]=4$. The edge supplies the required <directed path> and $f[u]>f[v]$, yet $d[u]>d[v]$. A path to an already black <vertex> need not put the two <vertices> into one discovery <tree>.