不含相邻短圈的可嵌入图的线性荫度  

Linear arboricity on embedded graphs without adjacent short cycles

作　　者：杜红军 王慧娟 DU Hongjun;WANG Huijuan(School of Mathematics and Statistics,Qingdao University,Qingdao 266071,Shandong,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071

出　　处：《山东大学学报（理学版）》2023年第11期147-154,共8页Journal of Shandong University(Natural Science)

基　　金：山东省自然科学基金资助项目(ZR2020MA045)。

摘　　要：线性荫度是一种非正常的边染色,图的线性荫度是指将它的边集划分为线性森林的最小数目。利用权转移方法,证明得到:对于任意的一个最大度Δ≥7的可嵌入到欧拉示性数非负的曲面图G而言,如果存在着两个固定的整数i,j∈{3,4,5,6},使得图G中不包含相邻的i-圈和j-圈,那么它的线性荫度是[Δ/2]。Linear arboricity is an improper edge coloring.The linear arboricity of a graph refers to the minimum number that the edge set is divided into linear forests.By using discharging method,we proved a conclusion about a graph G which can be embedded in a surface of non-negative Euler characteristic with maximum degreeΔ≥7.If there exist two fixed integers i,j∈{3,4,5,6}such that G has no adjacent i-cycles or j-cycles,then its linear arboricity is「Δ/2.

关 键 词：欧拉示性数 曲面 线性荫度 

分 类 号：O157.5[理学—数学]