• 应用数学与基础数学 •

### 较大亏格曲面嵌入图的线性荫度

1. 枣庄学院~~数学与统计学院, 山东~~枣庄 277160
• 收稿日期:2012-04-01 修回日期:2012-07-01 出版日期:2013-01-25 发布日期:2013-01-18

### Linear arboricity of an embedded graph on a surface of large genus

LV Chang-qing,  FANG Yong-lei

1. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang Shandong 277160, China
• Received:2012-04-01 Revised:2012-07-01 Online:2013-01-25 Published:2013-01-18

$\Delta(G)\geq (\sqrt{45-45\varepsilon}+10)$\,且不含\,4-圈,

$\Sigma$\,是亏格为\,$k(k>2)$\,的不可定向曲面时 $\varepsilon=2-k$.

Abstract: The linear arboricity of a graph $G$ is the minimum number
of linear forests which partition the edges of $G$. This paper
proved that if $G$ can be embedded on a surface of large genus
without 4-cycle and $\Delta(G)\geq (\sqrt{45-45\varepsilon}+10)$,
then its linear arboricity is $\lceil \frac{\Delta}{2}\rceil$, where
$\varepsilon=2-2h$ if the orientable surface with genus
\,$h(h>1)$\,or $\varepsilon=2-k$ if the nonorientable surface with
genus \,$k(k>2)$. It improves the bound obtained by J. L. Wu. As an
application, the linear arboricity of a graph with fewer edges were
concluded.