On the vertex-arboricity of planar

被引：55
|
作者：
Raspaud, Andre [1 ]
Wang, Weifan [1 ]
机构：
[1] Univ Bordeaux 1, CNRS, UMR 5800, LaBRI, F-33405 Talence, France
来源：
EUROPEAN JOURNAL OF COMBINATORICS | 2008年 / 29卷 / 04期
关键词：
D O I：
10.1016/j.ejc.2007.11.022
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The vertex-arboricity a (G) of a graph G is the minimum number of subsets into which the set of vertices of G can be partitioned so that each subset induces a forest. It is well-known that a (G) :! 3 for any planar graph G. In this paper we prove that a (G) <= 2 whenever G is planar and either G has no 4-cycles or any two triangles of G are at distance at least 3. (c) 2007 Elsevier Ltd. All fights reserved.
引用
收藏
页码：1064 / 1075
页数：12
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