关于生成迹在闭包运算下的稳定性

On Stability of the Spanning Trial under the Closure

证明了如果在图G的闭包中可以找到一个以某确定顶点为端点的生成迹当且仅当在G中可以找到一个以该顶点为端点的生成迹,得出了无爪图中生成迹的存在性在Ryjacek闭包运算下是稳定的,也就是一个无爪图G存在一个生成迹当且仅当图G的闭包cl(G)存在一个生成迹.

In the class of claw-free graphs,the stabilities of lots of properties under the closure defined by Ryjacek have been studied in former papers.In this paper,it is proved that the existence of a spanning trail,in a claw-free graph,is stable under the closure,i.e.,a claw-free graph G has a spanning trail if and only if the closure cl（G） of G has a spanning trail.