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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
##### Keywords:
digraph; dicycle; short cycles; degrees; directed graph; directed cycle
Full Text:
##### References:
 [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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