不含相交5-圈的平面图的线性2-荫度

Linear 2-arboricity of planar graphs without intersecting 5-cycles

设G是不含相交5-圈的平面图,证明了如果G是连通的并且δ(G)≥2,则G包含一条边xy,使得d(x)+d(y)≤10或者一个2-交错圈。由这个结果可以得到G的线性2-荫度la2(G)≤「Δ/2■+5,改进了不含5-圈的平面图的线性2-荫度的已知上界。

Let G be a planar graph without intersecting 5-cycles.If G is connected andδ(G)≥2,then G contains an edge xy with d(x)+d(y)≤10 or a 2-alternating cycle is proved.By this result,its linear 2-arboricity la2(G)≤「Δ/2■+5 is obtained,which improves the known upper bound of la2(G)for planar graphs without 5-cycles.