Bipartite graphs containing every possible pair of cycles

Abstract Let G=(V 1 ,V 2 ;E) be a bipartite graph with |V 1 |=|V 2 |=n⩾4 . Suppose that d(x)+d(y)⩾n+2 for all x∈V 1 and y∈V 2 . Then G contains two vertex-disjoint cycles of lengths 2s and 2t , respectively, for any two positive integers s and t with s⩾2 , t⩾2 and s+t⩽n . We also propose a conjecture.