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Decomposing $$k$$-arc-strong tournaments into strong spanning subdigraphs. (English) Zbl 1064.05067
The Kelly conjecture states that every regular tournament on $$2k+1$$ vertices has a decomposition into $$k$$ arc-disjoint Hamiltonian cycles. The authors formulate a generalization of this conjecture, i.e., every $$k$$-arc-strong tournament contains $$k$$ arc-disjoint spanning strong subdigraphs. Several results supporting this conjecture are proved.

##### MSC:
 05C20 Directed graphs (digraphs), tournaments 05C38 Paths and cycles 05C40 Connectivity 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
##### Keywords:
Hamiltonian cycles; decomposition; Kelly conjecture
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