Long cycles in bipartite graphs

AbstractLet G be a 2-connected bipartite graph with bipartition (A, B), where |A| ≥ |B|. It is shown that if each vertex of A has degree at least k, and each vertex of B has degree at least l, then G contains a cycle of length at least 2min(|B|, k + l − 1, 2k − 2). Then this result is used to determine the minimum number of edges required in a bipartite graph to ensure a cycle of length at least 2m, for any integer m ≥ 2