Hamilton连通的一个充分条件

A SUFFICIENT CONDITION FOR HAMILTON-CONNECTEDGRAPH

证明了如下结果：设Ｇ是阶为ｎ（≥１１）的３－连通图，若对Ｇ的所有距离为２的顶，点ｕ、ｖ，都有ｄ（ｕ）＋ｄ（ｖ）≥ｎ－１或｜Ｎ（ｕ∩Ｎ（ｖ）｜α＋１或｜（ｕ）∪Ｎ（ｖ）｜≥ｎ－δ＋１．则Ｇ是Ｈａｍｉｌｔｏｎ连通的。除非Ｇ属于一些特殊图类。

Under the assumption that G is let to be a 3-connected graph of ordern(n≥11),it has proved that,if for all vertices at an interval of 2 in between(i.e. ,d(u,v)=2) u and vforG,d(u)+d(v)≥n-lor|N(u)∩N(v)|1≥a+lor|N(u)∪N(v)|≥n-δ+1holds,then G is Hamilton-connected unless G belongs to some special groups of graphs.