## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Tuesday, March 28, 2017, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Matija Bucic

## Directed Ramsey number for trees

Given an oriented graph H, the k-colour oriented Ramsey number of H, denoted by R(H,k), is the least integer n, for which every k-edge-coloured tournament on n vertices contains a monochromatic copy of H. We show that R(T,k) < ck|T|k for any oriented tree T, which, in general, is tight up to a constant factor. We also obtain a stronger bound, when H is an arbitrarily oriented path. This is joint work with Shoham Letzter and Benny Sudakov.

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