本文研究的图 G 为简单的无向的二部图.所用术语和符号除说明外皆同[1].c(G)表示 G 的最长圈的长.以(A_1,A_2)为二分类的二部图记为 G(A_1,A_2).\delta=min{d(v)|v∈V(G)}.已有结果:定理1.设 G(A_1,A_2)为二连通的二部图,则 c(G)≥2min{|A_1|,|A_2|,2δ—2}.定理2.设 G(A_1,A_2)为二连通的二部图,且\delta_i=min{d(v)|v∈A_i}(i=1,...

Let G be a 2-connected bipartite graph with bipartition (A_1,A_2).If d(u,v)=2 and max {d(u),d(v)}≥δ~* for any u,v∈V (G),then G contains a cycleof length at least 2 min (|A_1|,|A_2|,2δ~*-2).Moreover,if |A_2|=|A_2|,δ~*≥1/2(|A_1|+1),then G has a Hamiltonian cycle.