Ramsey numbers for transitive tournaments Original Research Article

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 Cn, Sn and RTnh, respectively, denote the monotone cycle, the out-star and a rooted outgoing tree of height h on n vertices. Here, we find ρ(C3,Cn), ρ(RTn2,Sm) and ρ(D1,D2) for small acyclic digraphs D1 and D2.