【摘要】 线性k-森林是指一个图G,它的每个连通分支是长至多为k的路.图G的线性k-荫度是指使得G可以边划分成m个线性k-森林的最小整数m,用lak(G)表示.本文探讨特殊平面图的线性二荫度,得到的结论有:1)每个3-圈不重边的平面图G,有la2(G)≤「Δ(G)/2﹁+10;2)每个3-圈不重点的平面图G,有la2(G)≤「Δ(G)/2﹁+7;3)每点至多关联「Δ(G)/2﹁个3-面的平面图G,有la2(G)≤「Δ(G)/2﹁+10.更多还原

【Abstract】 A linear k-forest is a graph whose components are paths of length at most k.The linear k-arboricity of G,denoted by lak(G), is the least integer m such that G can be edge-partitioned into m linear k-forests.Let G be a planar graph.This paper proves that 1) la2(G)≤「Δ(G)/2?+10 if any two 3-cycles of G has nocommon edge; 2) la2(G)≤「Δ(G)/2?+7 if any two 3-cycles of G has no common vertex; 3) la2(G)≤「Δ(G)/2?+10 if every vertex of G is adjacent to at most 「Δ( G)/2? 3-faces.更多还原