%0 Journal Article
%T 嵌入曲面的图的点荫度<br>On the vertex-arboricity of embedded graphs
%A 孙林
%A 蔡华&lt
%A br&gt
%A SUN Lin
%A CAI Hua
%J 山东大学学报（理学版）
%D 2015
%R 10.6040/j.issn.1671-9352.0.2014.324
%X 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.<br>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
%K 点荫度
%K 放电法
%K 距离
%K &lt
%K br&gt
%K discharging method
%K vertex arboricity
%K distance
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2014.324