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.