Strong Erdős–Hajnal property for the directed triangle
Let the directed triangle mean the cyclic tournament on three vertices, and say that a tournament has the Strong Erdős–Hajnal property when it satisfies the strong Erdős–Hajnal conjecture. Directed-triangle conjecture. The directed triangle has the Strong Erdős–Hajnal property.
This is presented as a special case of the strong Erdős–Hajnal conjecture. The supplied text does not state whether this special case has been resolved.
References
Primary source
Ararat Harutyunyan, Colin McDiarmid and Gil Puig i Surroca, “Acyclic sets and colorings in digraphs under restrictions on degrees and cycle lengths”, arXiv:2603.02947 (2026).
Additional references
2 papers in this index state this conjecture (2023–2026). The statement above is taken from the most recent of them; the others are arXiv:2310.04265.
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