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 Haggkvist in 1978 that e = 1/3. Recently Bondy showed that c ≤ (2 6~(1/2) - 3)/5 = 0.3797… by using some counting arguments. In this note,we proved that c ≤ 3 - 7~(1/2) = 0.3542…
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