Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 7 / b / i / Solution

False. Take two vertices $u,v$ with both directed edges, and start depth-first search at $v$. The timestamps are $d[v]=1$, $d[u]=2$, $f[u]=3$, $f[v]=4$. There is an edge, hence a directed path, from $u$ to $v$, but $f[u]<f[v]$. Reaching a gray ancestor does not make the ancestor finish first.