On the k-anti-traceability Conjecture

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≤ 4. We also show that every sufficiently large k-anti-traceable oriented graph admits an anti-path that contains $n-o(n)$ vertices.