Ramsey numbers for transitive tournaments

Let D1,D2, . . . ,Dk be acyclic digraphs. Define ρ(D1,D2, . . . ,Dk) to be the minimum integer n such that every k-colouring of the transitive tournament TTn contains a monochromatic Di for some i. Let script capital Cn, Sn and RThn, respectively, denote the monotone cycle, the out-star and a rooted outgoing tree of height h on n vertices. Here, we find ρ(script capital C3, script capital Cn), ρ(RT2n, Sm) and ρ(D1, D2) for small acyclic digraphs D1 and D2. © 1999 Elsevier Science B.V. All rights reserved.