Hamilton图的充分条件

从1952年Dirac定理开始,Hamilton图的充分条件通常沿着边密度条件发展。Ore定理放宽了Dirac条件而且推广了控制图中顶点度的方法;进一步,Fan定理打开了一个全新的研究道路——尽管还是稠密性条件,但渗入某些局部化结构。1989年,Faudree等人提出了邻域并条件,近几年许多新结果不断涌现。文中,我们推广了上述结果,提出新的Hamilton图的充分条件。

The Sufficient Conditions for a Hamiltonian Graph.

From the Dirac's theorem in 1952,the approach taken to devel-oping sufficient conditions for a hamiltonian graph usually involved some sortof edge density condition ; Ore's theorem relaxed Dirac's condition and ex-tentde the methods for controlling the degrees of the vertices in the graph.Furthermore, Fan's theorem opened an entirely new avenue for investigation-one that incorporates some of the local structure, along with a densitycondition. In 1989, Faudree et al. presented neighborhood union condition,many new results have been discovered in the last few years. In this paper,we will obtain a generalization of above results and prove new sufficient con-ditions for a hamiltonian graph.