We prove that, with high probability, any 2-edge colouring of a random tournament on n vertices contains a monochromatic path of length Ω(n/logn). 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.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- directed paths
- edge colouring
- Random tournament
- Size Ramsey number