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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.)
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