关于Hamilton图的新的圈结构定理

A new cycle structure theorem for Hamiltonian graphs

设G是一个n阶图,若对于每一个k (3≤k≤n),图G都含有k-圈,则称图G为泛圈图.泛圈图是圈理论研究中的重要课题.研究得到了Hamilton圈上两个不相邻的点在圈上的距离是3的泛圈性结果.

An n-vertex graph is called pancyclic if it contains a cycle of length k for every k(3≤k≤n).Pancyclic graphs are an important topic in cycle theory.In this paper,we demonstrate pancyclicity by showing that the distance between two non-adjacent vertices on a Hamiltonian cycle is 3.