The Ramsey numbers for disjoint unions of trees

For given graphs G and H, the Ramsey numberR(G,H) is the smallest natural number n such that for every graph F of order n: either F contains G or the complement of F contains H. In this paper, we investigate the Ramsey number R(@?G,H), where G is a tree and H is a wheel W"m or a complete graph K"m. We show that if n>=3, then R(kS"n,W"4)=(k+1)n for k>=2, even n and R(kS"n,W"4)=(k+1)n-1 for k>=1 and odd n. We also show that R(@?"i"="1^kT"n"""i,K"m)=R(T"n"""k,K"m)+@?"i"="1^k^-^1n"i.