Injective coloring of planar graphs with girth 5

被引：0

作者：

Bu, Yuehua ^{[1
,2
]}

Yang, Qiang ^{[1
]}

Zhu, Junlei ^{[3
]}

Zhu, Hongguo ^{[1
]}

机构：

[1] Zhejiang Normal Univ, Dept Math Sci, Jinhua 321004, Zhejiang, Peoples R China

[2] Zhejiang Guangsha Vocat & Tech Univ Construction, Dept Basics, Jinhua 322100, Zhejiang, Peoples R China

[3] Jiaxing Univ, Coll Data Sci, Jiaxing 314001, Zhejiang, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 07期

关键词：

injective coloring; planar graph; cycle;

D O I：

10.3934/math.2023872

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A k-injective-coloring of a graph G is a mapping c : V (G) -> [1, 2, center dot center dot center dot , k} such that c (u) # c (v) for any two vertices u and v if u and v have a common vertex. The injective chromatic number of G, denoted by chi i (G), is the least k such that G has an injective k-coloring. In this paper, we prove that for planar graph G with g (G) >= 5, Delta (G) >= 20 and without adjacent 5-cycles, chi i (G) <= Delta (G) + 2.

引用

页码：17081 / 17090

页数：10

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