最大度大于等于9的IC-平面图的线性荫度  

The Linear Arboricity of IC-Planar Graphs

作　　者：张董董 李永杰 刘娟[1] Zhang Dongong;Li Yongjie;Liu Juan(School of Big Data Science,Jiangxi Science&Technology Normal University,Nanchang 330038,Jiangxi,P.R.China)

机构地区：[1]江西科技师范大学大数据科学学院,江西南昌330038

出　　处：《江西科技师范大学学报》2023年第6期88-94,共7页Journal of Jiangxi Science & Technology Normal University

基　　金：江西科技师范大学博士启动基金(2021BSQD29);江西省教育厅科技项目(GJJ211144)。

摘　　要：图的线性荫度la(G)是指能够使得G的边集可以被划分成m个边不交的线性森林的最小的m。1-平面图是指一个图画在平面上使得每条边与其他边至多相交一次。IC-平面图是指1-平面图的任意两个交叉点所关联的交叉边的端点是互不相交的。本文证明了Δ(G)≥9的IC-平面图满足线性荫度猜想。The linear arboricity la(G)of the graph is the least integer m that allows the set of edges of G to be divided into m edge-disjoint forests.A graph is called 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge.IC-planar graph is a 1-planar graph satisfying the condition that each vertex is incident with at most one crossing edge.In this paper,we prove the conjecture is true for IC-planar graphs withΔ(G)≥9.

关 键 词：图论 1-平面图 IC-平面图 线性荫度 

分 类 号：O157.5[理学—数学]