Injective coloring of planar graphs with girth 5

doi:10.1007/s11464-022-1018-x

Front. Math. China

2022, Vol. 17

Issue (3) : 473-484 https://doi.org/10.1007/s11464-022-1018-x

RESEARCH ARTICLE

Injective coloring of planar graphs with girth 5

Yuehua BU^1,²(

), Piaopiao YE¹

¹. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
². Xingzhi College, Zhejiang Normal University, Jinhua 321004, China

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Abstract

A coloring of a graph $G$ is injective if its restriction to the neighbour of any vertex is injective. The injective chromatic number $X i (G)$ of a graph $G$ is the least $k$ such that there is an injective $k$ -coloring. In this paper, we prove that for each planar graph with $g ≥ 5$ and $Δ (G) ≥ 20$ , $χ i (G) ≤ Δ (G) + 3$ .

Keywords Planar graph girth injective coloring face

Corresponding Author(s): Yuehua BU

Issue Date: 25 May 2022

Cite this article:

Yuehua BU,Piaopiao YE. Injective coloring of planar graphs with girth 5[J]. Front. Math. China, 2022, 17(3): 473-484.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-022-1018-x
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I3/473

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