1-退化图的乘积图的线性荫度  

Linear arboricity of product graphs of 1-degenerate graphs

作　　者：刘兆志 买吐肉孜·买司地克 LIU Zhaozhi;Metrose Metsidik(School of Mathematical Science,Xinjiang Normal University,Urumqi 830017,Xinjiang,China)

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830017

出　　处：《山东大学学报(理学版)》2025年第2期51-62,共12页Journal of Shandong University(Natural Science)

基　　金：新疆少数民族科技人才特殊培养计划科研项目(2022D03002);国家自然科学基金资助项目(11961070)。

摘　　要：由因子图的退化度来刻画乘积图的退化度,再结合关于退化图线性荫度的结论,给出笛卡尔积图和部分直积图、强积图满足线性荫度猜想的退化度条件。证明2个1-退化图字典积图满足线性荫度猜想,并给出其在大部分情况下的线性荫度。In this paper,we describe the degeneracy of the product graphs by the degeneracy of their factor graphs,combined with conclusions on the linear arboricity of degeneracy graphs,and give the degeneracy conditions for Cartesian product graphs,some direct product graphs and strong product graphs to satisfy the linear arboricity conjecture.Then we prove that the lexicographic product graph of two 1-degenerate graphs satisfies the linear arboricity conjecture and determine its linear arboricity in most cases.

关 键 词：线性荫度猜想 退化图 笛卡尔积 直积 字典积 

分 类 号：O157.5[理学—数学]