Liang, Hao; Xu, Junming A note on Caccetta-Häggkvist conjecture. (Chinese. English summary) Zbl 1299.05146 Acta Math. Sin., Chin. Ser. 56, No. 4, 479-486 (2013). Summary: L. Caccetta and R. Häggkvist [in: Proc. 9th Southeast. Conf. on combinatorics, graph theory, and computing, Boca Raton 1978, 181–187 (1978; Zbl 0406.05033)] made an open conjecture: any digraph on \(n\) vertices with minimum outdegree at least \(r\) contains a directed cycle of length at most \([n/r]\). We prove that if \(\alpha\geq 0.28724\), then any digraph on \(n\) vertices with minimum outdegree at least \(\alpha n\) contains a directed cycle of length at most 4. Cited in 1 Document MSC: 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles Keywords:digraph; directed cycle; Caccetta-Häggkvist conjecture Citations:Zbl 0406.05033 PDFBibTeX XMLCite \textit{H. Liang} and \textit{J. Xu}, Acta Math. Sin., Chin. Ser. 56, No. 4, 479--486 (2013; Zbl 1299.05146)