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中文摘要：
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.
英文摘要：
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 Δ（G）≥（（45-45ε）~（1/2）＋10）, then its linear arboricity is [Δ/2], where ε=2-2h if the orientable surface with genus h（h 〉 1） or ε=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.
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