Let G = (V-1, V-2, E) be a balanced bipartite graph with 2n vertices. The bipartite binding number of G, denoted by B(G), is defined to be n if G = K-n,K-n and min(i is an element of {1,2}) min (empty set not equal S subset of Vi vertical bar N(S)vertical bar < n) vertical bar N(S)vertical bar/vertical bar S vertical bar otherwise. We call G bipancyclic if it contains a cycle of every even length m for 4 = 139, then G is bipancyclic; the bound 3/2 is best possible in the sense that there exist infinitely many balanced bipartite graphs G that have B(G) = 3/2 but are not Hamiltonian.
