2-连通无爪图的Hamilton性

Hamilton problem of 2-connected claw-free graphs

Hamilton问题是图论中重要的问题之一,已经得到了很多很好的结果,但一个图是Ham-ilton图的充分必要条件到现在还没有得出,文章应用幅度的概念,使用反证法,通过构造最长圈并得出矛盾的方法,给出了2-连通无爪图,若θ(G)21(n-δ-2)时,G为Hamilton图这一充分条件,为进一步讨论Hamilton提供了一种新的思路。

Hamilton problem is one of the most important problems in Graph Theory. We have had many achievements, but there is not the result of the sufficient and necessary condition that a graph is a Hamiltonian graph. In this paper, we introduced the definition of spoke number, by the way of reduction to absurdity, we get the following result. If ,then 2-connected claw-free graph G is a Hamiltonian graph. The result of this paper can help people to provide a new method to study claw free graphs and the relation of spoke number and Hamilton property.