  An oriented graph is called $k$-anti-traceable if the subdigraph induced by
every subset with $k$ vertices has a hamiltonian anti-directed path. In this
paper, we consider an anti-traceability conjecture. In particular, we confirm
this conjecture holds when $k\leq 4$. We also show that every sufficiently
large $k$-anti-traceable oriented graph admits an anti-path that contains
$n-o(n)$ vertices.
