科研之友
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摘要
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. We prove that r(h, k) = (h - 1)(k) for all k sufficiently large (k = Theta(h log h) suffices). The bound (h - 1)(k) is tight. The related parameter r*(h, k) where some color contains all oriented trees is asymptotically determined. Values of r(h, 2) for some small h are also established.
- 出版日期2017-2
