Jackson's Hamilton decomposition conjecture for regular bipartite tournaments

A regular bipartite tournament is an orientation of the complete balanced bipartite graph K2n,2nK_{2n,2n} in which every vertex has indegree and outdegree nn. A Hamilton decomposition is a decomposition of all directed edges into Hamilton cycles. Jackson's conjecture. Any regular bipartite tournament can be decomposed into Hamilton cycles. Jackson's conjecture concerns the existence of a spanning cycle decomposition in the most balanced bipartite tournament setting. Jackson proved that every regular bipartite tournament is Hamiltonian; the decomposition assertion is the remaining conjectural strengthening addressed by this paper.

Sources & referencesView supporting material

Primary source

Bertille Granet, “Hamilton decompositions of regular bipartite tournaments”, arXiv:2209.02988 (2022).

Additional references

5 papers in this index state this conjecture (2009–2022). The statement above is taken from the most recent of them; the others are arXiv:1907.08479, arXiv:1402.4268, arXiv:1203.0659, arXiv:0908.3411.

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