Manoussakis's pancyclicity conjecture for digraphs
Manoussakis's pancyclicity conjecture for digraphs
Let be a strongly connected digraph on vertices. For vertices , say that is nonadjacent to when neither arc between them is present. A digraph is pancyclic if it contains directed cycles of every length allowed by the conjecture.
Manoussakis's conjecture. If, for every triple with nonadjacent to , the inequalities
when , and
when , hold, then is pancyclic.
This is a proposed pancyclic analogue of Manoussakis-type Hamiltonicity degree conditions. The supplied source does not report a resolution.
Sources & referencesView supporting material
Primary source
Bo Ning, “Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs”, arXiv:1404.5013 (2014).
Progress summary
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