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Every tournament of dichromatic number $10 k^2$ has a vertex whose out-neighborhood has dichromatic number more than $k$
The dichromatic number of a tournament is the minimum number of colors needed to color the vertices so that no directed cycle is monochromatic. Nguyen, Scott, and Seymour (2025) asked whether every tournament with dichromatic number $2k$ has a vertex whose out-neighborhood induces a subtournament of
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