The Ramsey numbers for disjoint unions of trees

For given graphs G and H, the Ramsey number R(G,H) is the smallest natural number n such that for every graph F of order\ud 9 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\ud is a tree and H is a wheel Wm or a complete graph Km. We show that if n 3, then R(kSn,W4) = (k + 1)n for k 2, even n and\ud R(kSn,W4) = (k + 1)n ??? 1 for k 1 and odd n.We also show that R(\ud \ud k\ud i=1Tni,Km) = R(Tnk,Km) +\ud \ud k???1\ud 11 i=1 ni