Abstract
Chung and Liu defined the d-chromatic Ramsey numbers as a generalization of Ramsey numbers by replacing the usual condition with a slightly weaker condition. Let 1<d<c and let . Assume A 1, A 2, …, A t are all d-subsets of a set containing c distinct colours. Let G 1, G 2, …, G t be graphs. The d-chromatic Ramsey number denoted by is defined as the least number p such that, if the edges of the complete graph K p are coloured in any fashion with c colours, then for some i, the subgraph whose edges are coloured by colours in A i contains a G i . In this paper, we determine for t=3, 4 and for linear forests G i , 1≤i≤t, when G 1 has at most one odd component and G j , 2≤j≤t−1, either is a path or has no odd component. Consequently, these numbers are determined when G i , 1≤i≤t, is either a path or a stripe.