Graph Theory With Applications
Graph Theory With Applications
| Hi-index | 0.05 |
Let D1,D2,...,Dk be simple digraphs with no directed cycles. The ordered Ramsey number ρ(D1,D2,...,Dk) is the least integer n such that every k-arc-colouring (C1,C2,...,Ck) of the transitive tournament TTn on n vertices contains a Ci-coloured Di for some i, 1 ≤ i ≤ k. This definition is useful in stating several classical theorems in combinatorics in a unified way and looking at their possible generalizations. Let Sn, S'n, Pn and tn, respectively, denote the out-star, in-star, directed path and an oriented tree on n vertices. In this paper, among other things we find ρ(tm, TTn), ρ(D, Pn2, Pn3,...,Pnk),ρ(Sm, S'n), where D is any weakly connected acyclic digraph on n1 vertices.