可嵌入到欧拉示性数非负的曲面图的线性荫度

Linear arboricity of graphs embedded in a surface of non-negative Euler characteristic

图G的线性荫度是一种非正常的边染色,即它的边集合E(G)可以分割成线性森林的最小数量,用la(G)表示。主要研究最大度Δ(G)≥7且可嵌入到欧拉示性数非负曲面图G上的线性荫度,证明了如果图G中不含相邻的含弦6-圈,则图G的线性荫度为「Δ/2」。

The linear arboricity of graph G,denoted by la( G),is the minimum number of linear forest required to partition the edge set E( G),which is an improper edge coloring. The linear arboricity of graph which can be embedded in a surface of non-negative Euler characteristic with maximum Δ( G) ≥7 is mainly studied. If there is no adjacent chordal 6-cycle,then the arboricity of graph G is「Δ/2」.