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).<\/p>\n
Already the value r(h,1) is a longstanding open problem which is not yet resolved for all h.<\/p>\n
We prove that r(h,k) = (h-1)^k for all k sufficiently large (in fact k=\\Theta(h \\log h) suffices).<\/p>\n
All notions will be explained.<\/p>\n","protected":false},"excerpt":{"rendered":"
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…
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