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A note on short cycles in digraphs. (English) Zbl 0626.05021
Caccetta and Häggkvist have conjected that a directed graph \(D_ n\) with minimum out-degree k must contain a directed cycle of length at most \(\lceil n/k\rceil\). The conjecture is known to be true when \(k\leq 3\). The authors of the present paper describe a proof for the cases when \(k\leq 5\).
Reviewer: J.W.Moon

MSC:
05C20 Directed graphs (digraphs), tournaments
05C38 Paths and cycles
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[1] Caccetta, L; Haggkvist, R, On minimal diagraphs with given girth, (), 181-187
[2] Chvátal, V; Szemerédi, E, Short cycles in directed graphs, J. combin theory ser. B, 35, 323-327, (1983) · Zbl 0545.05038
[3] Y.Y. Hamildoune, On girth in digraphs, to appear.
[4] C. Thomassen, On 2-linkages in acyclic digraphs, to appear. · Zbl 0563.05027
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