| 平面图点荫度的一个局部条件 |
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| 引用本文： | 黄丹君,凌银.平面图点荫度的一个局部条件[J].数学进展,2020(2):146-158. |
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| 作者姓名： | 黄丹君 凌银 |
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| 作者单位： | 浙江师范大学数学与计算机科学学院 |
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| 基金项目： | 浙江省自然科学基金(No.LY18A010014)。 |
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| 摘 要： | 图G的点荫度va(G)是指V(G)的最小划分数,使得每个点划分集的导出子图是一个森林.众所周知,平面图G的点荫度至多为3.2008年,Raspaud和王维凡证明了:若G是不含κ-圈(κ∈{3,4,5,6})的平面图,则va(G)≤2.本文推广了上述结果,得到了点荫度至多为2的一个局部条件,即若平面图G的每一个点都不同时与3-圈、4-圈、5-圈和6-圈关联,则va(G)≤2.
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| 关 键 词： | 平面度 点荫度 染色 圈 |
A Local Condition on the Vertex-arboricity of Planar Graphs |
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| HUANG Danjun,LING Yin.A Local Condition on the Vertex-arboricity of Planar Graphs[J].Advances in Mathematics,2020(2):146-158. |
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| Authors: | HUANG Danjun LING Yin |
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| Institution: | (College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua,Zhejiang,321004,P.R.China) |
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| Abstract: | The vertex-arboricity va(G) of a graph G is the minimum number of partitions of vertices,so that each partition induces a forest.It is well known that va(G)≤3 for any planar graph G.In 2008,Raspaud and Wang proved that if G is a planar graph and does not containκ-cycle,κ∈{3,4,5,6},then va(G)≤2.In this paper,we obtain a new local condition.That is:if any vertex of planar graph G is not simultaneously incident with 3-cycle,4-cycle,5-cycle and 6-cycle,then va(G)≤2. |
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| Keywords: | planar graph vertex-arboricity coloring cycle |
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