On long cycles in a 2-connected bipartite graph

Let k be an integer with k greater than or equal to 2. Let G = (A, B; E) be a 2-connected bipartite graph. Suppose d(x) + d(y) greater than or equal to k + 1 for every pair of non-adjacent vertices x and y. Then G contains a cycle of length at least min(2a, 2k) where a = min(\A\, \B\), unless G is one of some known exceptions. We conjecture that if \A\ = \B\ and d(x) + d(y) greater than or equal to k + 1 for every pair of non-adjacent vertices x and y with x is an element of A and y is an element of B, then G contains a cycle of length at least min(2a, 2k).