Some multicolor bipartite Ramsey numbers involving cycles and a small number of colors

For bipartite graphs G1,G2,…,Gk, the bipartite Ramsey number b(G1,G2,…,Gk) is the least positive integer b so that any coloring of the edges of Kb,b with k colors will result in a copy of Gi in the ith color for some i. In this paper, our main focus will be to bound the following numbers: b(C2t1,C2t2) and b(C2t1,C2t2,C2t3) for all ti≥3,b(C2t1,C2t2,C2t3,C2t4) for 3≤ti≤9, and b(C2t1,C2t2,C2t3,C2t4,C2t5) for 3≤ti≤5. Furthermore, we will also show that these mentioned bounds are generally better than the bounds obtained by using the best known Zarankiewicz-type result.