上可嵌入图与次上可嵌入图的线性荫度

The linear arboricity of upper-embedded graph and secondary upper-embedded graph

通过度再分配的方法研究上可嵌入图与次上可嵌入图的线性荫度,证明了最大度△不小于(4-3ε)^(1/3)且欧拉示性数ε≤0的上可嵌入图其线性荫度为「△/2」.对于次上可嵌入图,如果最大度△≥(4-3ε)^(1/3)且ε≤0,则其线性荫度为「△/2」.改进了文献[1]中最大度的的界.作为应用证明了双环面上的三角剖分图的线性荫度.

The linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G.In the present,it is proved that if a upper-embedded graph G has A ≥ 3√4-3ε then its linear arboricity is 「△/2（]） and if a secondary upper-embedded graph G has A ≥ 6√1-ε then its linear arboricity is「-△/2（]）,where ε ≤ 0.It improves the bound of the conclusion in [1].As its application,the linear arboricity of a triangulation graph on double torus is concluded.