The traceability conjecture for k-traceable oriented graphs

A digraph $D$ is $k$-traceable if its order is at least $k$ and each of its induced subdigraphs of order $k$ is traceable; an oriented graph is a digraph obtained by orienting the edges of an undirected graph, and a digraph is traceable if it contains a hamiltonian directed path.

Traceability conjecture. For every integer $k\geq 2$, every $k$-traceable oriented graph of order at least $2k-1$ is traceable.

This conjecture extends Rédei's theorem that every tournament is traceable and strengthens results for strongly connected digraphs with independence number two. Its resolution status is not established by the supplied source material.