An Improved Upper Bound on the Linear 2-arboricity of 1-planar Graphs

作     者：Juan LIU Yi Qiao WANG Ping WANG Lu ZHANG Wei Fan WANG Juan LIU;Yi Qiao WANG;Ping WANG;Lu ZHANG;Wei Fan WANG

作者机构：Department of MathematicsZhejiang Normal UniversityJinhua 321004P.R.China School of ManagementBeijing University of Chinese MedicineBeijing 100029P.R.China Department of Mathematics and StatisticsSt.Francis Xavier UniversityAntigonishNova ScotiaCanada 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2021年第37卷第2期

页      面：262-278页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：1-planar graph linear 2-arboricity edge-partition maximum degree 

摘      要：The linear 2-arboricity la2(G) of a graph G is the least integer k such that G can be partitioned into k edge-disjoint forests,whose component trees are paths of length at most 2.In this paper,we prove that if G is a 1-planar graph with maximum degree Δ,then la_(2)(G)≤[(Δ+1)/2]+7.This improves a known result of Liu et al.(2019) that every 1-planar graph G has la_(2)(G)≤[(Δ+1)/2]+14.We also observe that there exists a 7-regular 1-planar graph G such that la2(G)=6=[(Δ+1)/2]+2,which implies that our solution is within 6 from optimal.