Monochromatic trees in random tournaments

Abstract

We prove that, with high probability, in every $2$-edge-colouring of the random tournament on $n$ vertices there is a monochromatic copy of every oriented tree of order $O(n/\sqrt{\log n})$. 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.

31 pages, 6 figures