树图的1-Hamilton连通性(英文)

1-Hamilton Connectedness of Tree Graphs

一阶数≥3的简单连通图叫做1-Hamilton连通的,若对每一对顶点v_1、v_2及任一边v_2v_3(v_1≠v_3),存在连接v_1和v_2,并且经过v_3v_2的Hamilton路.本文中我们证明:连通图的树图或是1-Hamilton连通的,或为一超立方体,或同构于K_2×K_3和W_5之一.

A connected simple graph Γ of order≥3 is said to be 1-Hamilton connected if for any pair of vertices v_1 and v_2 and every edge v_2v_3 (where v_1(?)v_3), there exists a Hamilton path of Γ connecting v_1 and v_2 and traversing v_2v_3. In this paper it is shown that the tree graph of a connected graph is either 1-Hamilton connected, or a hypercube, or isomorphic to one of K_2×K_3 and W_5, a wheel on 5 vertices.