A panconnectivity theorem for bipartite graphs

Let G be a simple m × n bipartite graph with m ≥ n . We prove that if the minimum degree of G satisfies δ ( G ) ≥ m ∕ 2 + 1 , then G is bipanconnected: for every pair of vertices x , y , and for every appropriate integer 2 ≤ l ≤ 2 n , there is an x , y -path of length l in G .