二连通二部图的偶泛圈性  

Bipancyclic of 2-Connected Bipartite Graphs

作　　者：马美杰[1] 戴珍香[1] 

机构地区：[1]烟台大学数学与信息科学系,山东烟台264005

出　　处：《烟台大学学报（自然科学与工程版）》2003年第4期239-243,共5页Journal of Yantai University(Natural Science and Engineering Edition)

摘　　要：范更华证明了如下结论:设G是具有n个点的二连通图(n≥3),若对任一对使d(u,v)=2的点有max{d(u),v(v)}≥π/2,则G是哈密顿圈的。将范氏条件限制在二部图上,已经得到二连通的二部图是哈密顿圈的一个类似充分条件。本文证明该充分条件亦保证了二部图的偶泛圈性:设二连通的平衡二部图G=(X,Y;E)每部有n个点,若对任一对使d(U,v)=2的点有max{d(u),d(v)}>π/2,则G为偶泛圈的。该结果是最好的可能。Let G be a 2-connected graph on n n≥ 3 vertices and let u and v be distinct vertices of G . Geng- hua Fan has proved that if d(u,v) = 2 implies max {d(u) ,d(v)|≥n/2, then G has a Hamiltonian cycle. Fan's condition and result are improved for the special case of bipartite graphs. That is : Let G = (X, Y;E) be a 2-connected bipartite graph with |X} =|Y | = n . Let M and v be distinct vertices of G. If d(u ,v) = 2 implies max {d(u) ,d(v)| > N/2 ,then G is bipancyclism. This result is, in a sense, best possible .

关 键 词：二部图 点度 二连通图 哈密顿圈 哈密顿圈 偶泛圈性 

分 类 号：O157.5[理学—数学]