The Size, Multipartite Ramsey Numbers for nK2 Versus Path-Path and Cycle

For given graphs G(1), G(2), ..., G(n) and any integer j, the size of the multipartite Ramsey number m(j) (G(1), G(2), ..., G(n)) is the smallest positive integer t such that any n-coloring of the edges of K-jxt contains a monochromatic copy of G(i) in color i for some i, 1 <= i <= n, where K-jxt denotes the complete multipartite graph having j classes with t vertices per each class. In this paper, we computed the size of the multipartite Ramsey numbers m(j) (K-1,K-2, P-4, nK(2)) for any j, n >= 2 and m(j) (nK(2), C-7), for any j <= 4 and n >= 2.