嵌入曲面的图的点荫度
On the vertex-arboricity of embedded graphs

摘要： 图G的导出森林k-划分是指其顶点集V(G)的一个k-划分(V1,V2,…,Vk),使得对于每个 i (1≤i≤k),导出子图G[Vi]是一个森林.图G的点荫度是使得图G有导出森林k-划分的最小的正整数k,记为va(G).主要证明了如果图G能够嵌入到欧拉示性数非负的曲面上,则当图G满足三类条件时,可以得到va(G)≤2.
Abstract: An induced forest k-partition of a graph G is a k-partition (V1,V2,…,Vk) of the vertex set V(G) such that, for each i with 1≤i≤k, the induced subgraph G[Vi] is a forest. The vertex arboricity of a graph G is the minimum positive integer k such that G has an induced forest k-partition, denoted by va(G). Let G be a simple graph embedded in a surface of nonnegative Euler characteristic, and if G satisfies three kinds of conditions, then va(G)≤2