  A complementation operation on a vertex of a digraph changes all outgoing
arcs into non-arcs, and outgoing non-arcs into arcs. A partially complemented
digraph $\widetilde{G}$ is a digraph obtained from a sequence of vertex
complement operations on $G$. Dahlhaus et al. showed that, given an
adjacency-list representation of $\widetilde{G}$, depth-first search (DFS) on
$G$ can be performed in $O(n + \widetilde{m})$ time, where $n$ is the number of
vertices and $\widetilde{m}$ is the number of edges in $\widetilde{G}$. To
achieve this bound, their algorithm makes use of a somewhat complicated
stack-like data structure to simulate the recursion stack, instead of
implementing it directly as a recursive algorithm. We give a recursive
$O(n+\widetilde{m})$ algorithm that uses no complicated data-structures.
