Bipartite graphs containing every possible pair of cycles Original Research Article

Let G=(V1,V2;E) be a bipartite graph with |V1|=|V2|=n⩾4. Suppose that d(x)+d(y)⩾n+2 for all x∈V1 and y∈V2. 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.