Behzad–Chartrand–Wall conjecture for oriented digraphs

Let $D$ be an $n$-vertex oriented digraph. Its minimum out-degree is the least number of outgoing neighbors of any vertex, and its minimum in-degree is the least number of incoming neighbors of any vertex. A directed triangle is a directed cycle of length three.

Behzad–Chartrand–Wall conjecture. Every $n$-vertex oriented digraph with minimum out-degree and minimum in-degree at least $n/3$ contains a directed triangle.

This is presented as a weakening of the $r=n/3$ case of the Caccetta–Häggkvist conjecture. The source states that it remains open.