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Cycles of all lengths in arc-3-cyclic semicomplete digraphs. (English) Zbl 0880.05056
A digraph of order $$n$$ is said to be arc-$$k$$-cyclic if every arc lies in a directed cycle of length $$k$$. It is said to be arc-pancyclic if it is arc-$$k$$-cyclic for each $$k\in\{3,4,\ldots,n\}$$. A digraph $$D$$ is said to be a semicomplete digraph if for every pair of distinct vertices $$u$$ and $$v$$ in $$D$$, at least one of $$(u,v)$$ or $$(v,u)$$ is an arc of $$D$$. The authors study arc-$$k$$-cyclicity and arc-pancyclicity of semicomplete digraphs.

##### MSC:
 05C38 Paths and cycles 05C20 Directed graphs (digraphs), tournaments
##### Keywords:
vertex-pancyclic; arc-pancyclic; tournament; digraph
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##### References:
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