关于图的星荫度的一个注

On the Vertex Star Arboricity of A Graph

图G的曼荫度vas(G)定度为对G进行项点着色且使得G中同色顶点导出的子图的每个连通分支都为星时所需的最少色数,本文证明了平面图和外平面图的曼荫度的平凡上界事实上也是最好的上界.

The vertex star arboricity vsa(G) of a graph G is defined as the minimum number of colors needed to color G such that each subgraph induced by the set of all vertices colored with same color has only stars as its components.In this note,It is proved that the trival upper bounds for vsa(G) of planar,outerplanar graphs are indeed best possible.