The order of hypotraceable oriented graphs

Grötschel, Thomassen, and Wakabayashi (Hypotraceable digraphs, J. Graph Theory 4 (1980) 377-381) constructed an infinite family of hypotraceable oriented graphs, the smallest of which has order 13. We show that the smallest hypotraceable oriented graph has 8 vertices and 15 arcs. We also show that there exist hypotraceable oriented graphs of order n for every n ≥ 8, except possibly for n = 9, 11. We apply these results to show that if 2 ≤ k ≤ 6 then every oriented graph of order at least k having the property that each of its subdigraphs of order k is traceable, is itself traceable. This result does not extend to k ≥ 7.