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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
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