Every tournament with minimum out-degree (2+o(1))k^2 contains a subdivision of the complete digraph on k vertices, and every tournament on C k^2 log^3 k vertices contains a 1-subdivision of the transitive tournament on k vertices.
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Subdivisions of digraphs in tournaments
Every tournament with minimum out-degree (2+o(1))k^2 contains a subdivision of the complete digraph on k vertices, and every tournament on C k^2 log^3 k vertices contains a 1-subdivision of the transitive tournament on k vertices.