Vertex-disjoint cycles of order eight with chords in a bipartite graph

Let G=(V1,V2;E) be a bipartite graph with ?V1?=?V2?=4k, where k is a positive integer. In this paper, it is proved that if the minimum degree of G is at least 3k+1, then G contains k vertex-disjoint cycles of order eight such that each of them has at least two chords.