Sumner's conjecture for oriented trees
Let be an oriented tree, let be its order, and let denote its unavoidability.
Sumner's conjecture. Every oriented tree of order is -unavoidable; equivalently,
This is a celebrated conjecture about tournaments and oriented trees. The source does not state a resolution, so its status remains open.
References
Primary source
Pierre Aboulker, Frédéric Havet, William Lochet, Raul Lopes, Lucas Picasarri-Arrieta and Clément Rambaud, “Blow-ups and extensions of trees in tournaments”, arXiv:2410.23566 (2024).
Additional references
5 papers in this index state this conjecture (2013–2024). The statement above is taken from the most recent of them; the others are arXiv:2310.18719, arXiv:1912.04004, arXiv:1812.05167, arXiv:1307.4803.
Progress summary
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Solutions 0
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