较大亏格曲面嵌入图的线性荫度

通过度再分配的方法研究嵌入到曲面上图的线性荫度.给定较大亏格曲面∑上嵌入图G,如果最大度Δ(G)≥((45-45ε)^(1/2)+10)且不含4-圈,则其线性荫度为Δ/2],其中若∑是亏格为h(h>1)的可定向曲面时ε=2-2h,若∑是亏格为k(k>2)的不可定向曲面时ε=2-k.改进了吴建良的结果,作为应用证明了边数较少图的线形荫度.

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

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.