4-圈不共点的平面图的线性2-荫度

Linear 2-arboricity of planar graphs with 4-cycles have no common vertex

图G的线性2-荫度la_2(G)是指可以使G分解为k个边不相交森林的最小整数k,其中森林的每个分支是长度至多为2的路。证明了若G是4-圈不共点的平面图,则la_2(G)≤「Δ/2■+5。

The linear 2-arboricity la2（G） of G is the least integer k to divide G into k edge-disjoint forests,and each branch of the forests is a path with the length at most 2. We prove that if G is a planar graph with 4-cycles without common vertex,then la2（G） ≤Δ/2 ＋ 5.