1-平面图的线性荫度  

Linear Arboricity of 1-planar Graphs

作　　者：黄丹君[1] 姜楠 Dan Jun HUANG;Nan JIANG(College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,P.R.China)

机构地区：[1]浙江师范大学数学科学学院,金华321004

出　　处：《数学学报（中文版）》2023年第2期339-352,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12171436)。

摘　　要：图G的边分解是指将G分解成子图G1,G2,…,Gm,使得E(G)=E(G1)∪…∪E(Gm),且对任意i≠j有E(Gi)∩E(Gj)=?.若一个森林的每个连通分支都是路,则称该森林为线性森林.图G的线性荫度la(G)是指使得G可以边分解为m个线性森林的最小整数m.本文利用权转移方法证明了Δ(G)≥25的1-平面图G的线性荫度为[Δ(G)/2],这里Δ(G)是图G的最大度.An edge-partition of a graph G is a decomposition of G into subgraphs G1,G2,…,Gmsuch that E(G)=E(G1)∪…∪E(Gm)and E(Gi)∩E(Gj)=?for any i≠j.A linear forest is forest in which each connected component is a path.The linear arboricity la(G)is the least integer m such that G can be edge-partitioned into m linear forests.In this paper,we use the discharging method to study the linear arboricity la(G)of 1-planar graphs,and prove that la(G)=「Δ(G)/2]for each 1-planar graph G withΔ(G)≥25,whereΔ(G)is the maximum degree of G.

关 键 词：1-平面图 边分解 线性荫度 

分 类 号：O157.5[理学—数学]