中文摘要：

线性k-森林是每一个连通分支均为长度不超过k的路的图。一个图G的线性k-荫度是将图G的边集合能分解成的线性k-森林的最少数目,用lak（G）来表示。证明了：若G为不含4-圈和5-圈的平面图,则la2（G）≤「Δ（G）＋1/2■＋4。

英文摘要：

A linear k-forest is a forest whose components are paths of length at most k.The linear k-arboricity of a graph G,denoted by lak（G）,is the least number of linear k-forests needed to decompose G.We have： if G is a plane graph without 4-cycles and 5-cycles,then la2（G）≤「Δ（G）＋1/2■＋4.