Monochromatic trees in random tournaments
Matija Bucic, Sven Heberle, Shoham Letzter, Benny Sudakov

TL;DR
This paper proves that in random tournaments with two-edge coloring, one can find monochromatic copies of all oriented trees up to size proportional to n divided by the square root of log n, extending previous path results.
Contribution
It generalizes prior work from paths to all oriented trees of a certain size in random tournaments, establishing tight bounds.
Findings
Monochromatic copies of all oriented trees of size O(n / sqrt(log n)) exist with high probability.
The result extends previous path-specific findings to more complex tree structures.
The bounds are tight up to a constant factor.
Abstract
We prove that, with high probability, in every -edge-colouring of the random tournament on vertices there is a monochromatic copy of every oriented tree of order . This generalises a result of the first, third and forth authors who proved the same statement for paths, and is tight up to a constant factor.
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