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An Algorithm for Finding a Maximum Cycle of Bipartite Graphs with Large Degrees

Let G be a simple bipartite graph with bipartition (X, Y) such that |X|≥|Y|≥2. Put n=|X|, m=|Y| and p=m+n. Suppose, for each pair of nonadjacent vertices x∈X and y∈Y we have d(x)+d(y)≥n+1. We give an efficient algorithm to obtain a cycle of length 2m in G. The complexity of this algorithm is O(p2). In particular, if m=n, we have a hamiltonian cycle of G.