For fixed integers m,k>=2, it is shown that the k-color Ramsey number r"k(K"m","n) and the bipartite Ramsey number b"k(m,n) are both asymptotically equal to k^mn as n->~, and that for any graph H on m vertices, the two-color Ramsey number r(H+K@?"n,K"n) is at most (1+o(1))n^m^+^1/(logn)^m^-^1. Moreover, the order of magnitude of r(H+K@?"n,K"n) is proved to be n^m^+^1/(logn)^m if H K"m as n->~.
['Yusheng Li', 'Xueqing Tang', 'Wenan Zang']
Ramsey functions involving Km,n with n large