Abstract: It is shown that r(W_m,K_n)≤l(1+o(1))C₁(m) (n/logn ) ^(2m-2)/(m-2)
for fixed even
r(W_m,K_n)≤(1+o(1))C₂(m) (n^2m/_m+1/^{_{log n)}(m+1)/(m-1)} for fixed odd m≥5 and n→∞. In particular, C₂(5)=12 . Also, c(ⁿ/_logn)^5/2≤r(K₄,K_n)≤ (1+o(1)) ^n3_/(logn)². Moreover, in this paper, the authors discuss some generalizations for wheel: complete graph Ramsey numbers.

Key words: Ramsey numbers, Wheels