Colloquium: Tuesday, April 18, 2 pm. Speaker: Raphael Yuster (Haifa). Title: “On the Ramsey number of oriented trees”.
Given positive integers h and k, denote by r(h,k) the smallest integer n such that in any k-coloring of the edges of a tournament on more than n vertices, there is a monochromatic copy of every oriented tree on h vertices. (In other words, r(h,k) is the k-color Ramsey number of oriented h-trees).
Already the value r(h,1) is a longstanding open problem which is not yet resolved for all h.
We prove that r(h,k) = (h-1)^k for all k sufficiently large (in fact k=\Theta(h \log h) suffices).
All notions will be explained.
