Behzad–Chartrand–Wall conjecture for oriented digraphs
Let be an -vertex oriented digraph. Its minimum out-degree is the least number of outgoing neighbors of any vertex, and its minimum in-degree is the least number of incoming neighbors of any vertex. A directed triangle is a directed cycle of length three.
Behzad–Chartrand–Wall conjecture. Every -vertex oriented digraph with minimum out-degree and minimum in-degree at least contains a directed triangle.
This is presented as a weakening of the case of the Caccetta–Häggkvist conjecture. The source states that it remains open.
References
Primary source
Hao Huang and Fei Peng, “An improved bound on Seymour's second neighborhood conjecture”, arXiv:2412.20234 (2024).
Additional references
4 papers in this index state this conjecture (2022–2024). The statement above is taken from the most recent of them; the others are arXiv:2401.14768, arXiv:2211.03129, arXiv:2207.05904.
Progress summary
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Solutions 0
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