Abstract
Let c be the smallest possible value such that every digraph on n vertices with minimum outdegree at least cn contains a directed triangle. It was conjectured by Caccetta and Häggkvist in 1978 that c =1/3. Recently Bondy showed that c ⩽(2 6 −3)/5=0.3797… by using some counting arguments. In this note, we prove that c ⩽3− 7 =0.3542….
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