Sumner's conjecture for oriented trees
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.
Sources & referencesView supporting material
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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