Kelly's conjecture on Hamiltonian decompositions of regular tournaments

A regular tournament is a tournament in which every vertex has the same indegree and outdegree. Kelly's conjecture. Every regular tournament on n=2k+1n=2k+1 vertices has a decomposition into kk arc-disjoint Hamiltonian cycles. The conjecture was proved for large nn by Kühn and Osthus; the source does not state a complete resolution for all nn.

Sources & referencesView supporting material

Primary source

Yuefang Sun, “Steiner Type Packing Problems in Digraphs: A Survey”, arXiv:2206.12092 (2026).

Additional references

7 papers in this index state this conjecture (2008–2022). The statement above is taken from the most recent of them; the others are arXiv:1902.10775, arXiv:1610.00117, arXiv:1006.0590, arXiv:0908.3411, arXiv:0901.3541, arXiv:0807.1827.

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