On long cycles in a 2-connected bipartite graph

Letk be an integer withk ≥ 2. LetG = (A, B; E) be a 2-connected bipartite graph. Supposed(x) + d(y) ≥ k + 1 for every pair of non-adjacent verticesx andy. ThenG contains a cycle of length at leastmin(2a, 2k) wherea = min(|A|,|B|), unlessG is one of some known exceptions. We conjecture that if|A| = |B| andd(x) + d(y) ≥ k + 1 for every pair of non-adjacent verticesx andy withx ∈ A andy ∈ B, thenG contains a cycle of length at leastmin(2a, 2k).