Multicolor Ramsey Numbers of Bipartite Graphs and Large Books

For graphs G and H, the Ramsey number r(k+1)(G; H) is defined as the minimum N such that any edge-coloring of K(N )by k+ 1 colors contains either a monochromatic G in the first k colors or a monochromatic H in the last color. A book B-n((m)) is a graph that consists of n copies of (Km+1) sharing a common K-m. We shall give upper bounds for r(k+1)(K-t,K-s; B-n((m))) and r(k+1)(C-2t; B-n((m)) ), some of which are sharp up to the sub-linear term asymptotically.