Monochromatic paths in random tournaments. Issue 1 (6th April 2018) - Bucić, Matija; Letzter, Shoham; Sudakov, Benny
Abstract: We prove that, with high probability, any 2‐edge‐coloring of a random tournament on n vertices contains a monochromatic path of length Ω ( n / 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.