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

页码：158 / 166

页数：9

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