Directed Triangles in Digraphs

Letcbe the smallest possible value such that every digraph onnvertices with minimum outdegree at leastcncontains a directed triangle. It was conjectured by Caccetta and Häggkvist in 1978 thatc=1/3. Recently Bondy showed thatc⩽(2 6−3)/5=0.3797… by using some counting arguments. In this note, we prove thatc⩽3−7=0.3542….