Hamilton偶图的局部度数条件

设Ｇ是具有二分类（Ｘ，Ｙ）的２连通等部偶图。如果对Ｇ中每一个顶点ｖ，Ｈ是Ｇ中与ｖ距离为２和３的所有顶点导出的子图，并且对于ｇ中每一个与ｖ距离为３的顶点ｕ，ｕ在Ｈ中的度数ｄ＿Ｈ（ｕ）不小于距离ｖ为２的顶点的数目减去（ｄＧ（ｖ）－２），则Ｇ是Ｈａｍｉｌｔｏｎ图。其中ｄ＿Ｈ（ｕ）的下界不能改进。

A Local Degree Condition for Hamiltonian Bipartite Graphs

Let G be a balanced 2-connected bipartite graph with bipartlition(X,Y). Suppose for each vertex v of G,H is the subgraph induced by the vertices which are dis- tance 2 or 3 from v,and for each vertex u which has distance 3 to v,the degree d_H(u)of uin H is at least the numbor of the vertices distance 2 from v minus(d_F(v)-2).Then Gis Hamiltonian,where the lower bound of d_H(u) is sharp.