The edge condition for independent cycles with chords in bipartite graphs

•In the study we investigate the edge condition for independent chorded cycles in bipartite graphs.•We present a constructive proof.•We study the structure of bipartite graphs which contain no specified independent chorded cycles. Let G=(V1,V2;E) be a bipartite graph with 3k≤m=|V1|≤|V2|=n, where k be a positive integer. We prove that if the number of edges of G is at least (4k−2)(n−2)+2m, then G contains k independent chorded cycles.