设G=(X,Y;E)是连通二部图,│X│= │Y│=n,则(1)NC2=n≥4,则G是点泛圈偶图。(2)NC2≥n-1≥4,且6≥2,则G含有Hamilton圈,或者G的任何一点都含在G中长为2n-2的圈中,且这个圈为G的控制圈。
Let G(X, Y;E) be a connected bipartite graph , │ X│=│Y│ = n, then ( 1 ) if NC2 = n ≥4, then G is vertex--pancyclic bipartite graph. (2)if NC2 =n-1≥4,andδ(G) ≥2, then G is Hamihonian, or ↓Au∈V(G), G has a C, │C│ =2n-2, u ∈ V( C), and C be domating cycle of G.