Planar graphs without 4-, 7-, 9-cycles and 5-cycles normally adjacent to 3-cycles

被引：0
|
作者：
Liu, Zhengjiao [1 ]
Wang, Tao [2 ]
Yang, Xiaojing [1 ]
机构：
[1] Henan Univ, Sch Math & Stat, Kaifeng 475004, Peoples R China
[2] Henan Univ, Ctr Appl Math, Kaifeng 475004, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2024年 / 358卷
基金：
中国国家自然科学基金;
关键词：
Planar graph; (I; F)-partition; Weak degeneracy; Transversal;
D O I：
10.1016/j.dam.2024.07.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A graph is (I,F)-partitionableif its vertex set can be partitioned into two parts suchthat one partIis an independent set, and the otherFinduces a forest. A graphisk-degenerateif every subgraphHcontains a vertex of degree at mostkinH.Bernshteyn and Lee defined a generalization ofk-degenerate graphs, which is calledweakly k-degenerate. In this paper, we show that planar graphs without 4-, 7-, 9-cycles,and 5-cycles normally adjacent to 3-cycles are both (I,F)-partitionable and weakly2-degenerate. (c) 2024ElsevierB.V.Allrightsarereserved,includingthosefortextanddatamining,AItraining,andsimilartechnologies.
引用
收藏
页码：158 / 166
页数：9
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