Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, March 16, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Shoham Letzter (ITS)

Long monochromatic paths in 2-coloured random tournaments

Given a tournament on n vertices, it is not hard to see that there is a 2-colouring of the edges such that the longest directed path has length O(n/sqrt(log n)). We show that for almost all tournaments, this bound is tight. I.e., for almost all tournaments, given any 2-colouring, there is a monochromatic directed path of length at least Omega(n/sqrt(log n)). This is joint work with Matija Bucić and Benny Sudakov.

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