Monochromatic paths in random tournaments

Abstract

We prove that, with high probability, any $2$-edge-colouring of a random tournament on $n$ vertices contains a monochromatic path of length $\Omega (n/\sqrt{\log n})$. This resolves a conjecture of Ben-Eliezer, Krivelevich and Sudakov and implies a nearly tight upper bound on the oriented size Ramsey number of a directed path.

Cited by in corpus (3)

• Directed Ramsey number for trees
• Monochromatic trees in random tournaments
• Path-monochromatic bounded depth rooted trees in (random) tournaments