最大平均度不超过4的图的线性2-荫度

Linear 2-arboricity of graphs with maximum average degree at most 4

一个2-线性森林是指每个分支均为长至多为2的路的图。将图G的边集合划分为m个线性2-森林的最小整数m,称为图G的线性2-荫度,记作la_2(G)。确定了mad(G)≤4的图的线性2-荫度的上界,若图G为mad(G)≤4的图,则la_2(G)≤「Δ(G)/2」+5(Δ(G)≡1,2(mod4));la2(G)≤「Δ(G)/2」+4(Δ(G)≡0,3(mod4))。

A linear 2-forest is a graph whose components are paths of length at most 2. The linear 2-arboricity of a graph G is the least integer m such that G can be partitioned into m linear 2-forests,denoted by la2（ G）. The upper bound of the linear 2-arboricity of graph G with mad（ G） ≤ 4 is determined and if G is a graph with mad（ G） ≤ 4,then la2（ G） ≤「Δ（ G）/2」＋ 5 if Δ（ G） ≡1,2（ mod 4） and la_2（ G） ≤「Δ（ G）/2」＋4 if Δ（ G） ≡0,3（ mod 4）.