AN OPTIMAL BINDING NUMBER CONDITION FOR BIPANCYCLISM.

Let G =(V1, V2, 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 = Kn,n and mini∈{1,2} min... |N(S)|/|S| otherwise. We call G bipancyclic if it contains a cycle of every even length m for 4 m 2n. The purpose of this paper is to show that if B(G) > 3/2 and n ≥ 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. [ABSTRACT FROM AUTHOR]