The m-bipartite Ramsey number of the K2,2 versus K6,6

For the given bipartite graphs G1, ... , Gn , the bipartite Ramsey number BR(G1, ... , Gn) is the least positive integer b such that any complete bipartite graph K-b,K-b having edges coloured with 1, 2, ... , n , contains a copy of some G(i) (1 <= i <= n), where all the edges of G(i) have colour i . For the given bipartite graphs G1, ... , Gn and a positive integer m , the m-bipartite Ramsey number BRm(G1, ... ,G(n)) is defined as the least positive integer b (b >= m) such that any complete bipartite graph K-m,K-b having edges coloured with 1, 2, ... , n , contains a copy of some G(i) (1 <= i <= n), where all the edges of G i have colour i . The values of BRm(G(1), G(2)) (for each m ), BRm(K-3,K-3,K- K-3,K-3 ) and BRm(K-2,K-2,K- K-2,K-2 K-5,K-5) (for particular values of m ) have already been determined in several articles, where G(1) = K-2,K-2 and G(2) is an element of { K-3,K-3 K-4,K-4} . In this article, the value of BRm(K-2,K-2, K-2,K-2 K-6,K-6) is computed for each m is an element of {2,3, ... , 8} .