AI Chat Paper
Note: Please note that the following content is generated by AMiner AI. SciOpen does not take any responsibility related to this content.
{{lang === 'zh_CN' ? '文章概述' : 'Summary'}}
{{lang === 'en_US' ? '中' : 'Eng'}}
Chat more with AI
Powered by AMiner. Clicking this button will take you away from SciOpen.
Home Journal of Xinjiang University(Natural Science Edition in Chinese and English) Article
PDF (3.7 MB)
Cite
EndNote(RIS) BibTeX
Collect
Submit Manuscript AI Chat Paper
Show Outline
Outline
Show full outline
Hide outline
Outline
Show full outline
Hide outline

Odd Chromatic Number of a 1-Planar Graph is at Most 21

School of Mathematics and System Sciences, Xinjiang University, Urumqi Xinjiang 830017, China
Show Author Information

Abstract

A proper vertex coloring φ of a graph G is said to be odd if for each non-isolated vertex x ∈ V(G) there exists a color c such that |φ−1(c)∩NG(x)| is odd. A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. We prove every 1-planar graph admits an odd 21-coloring. This improves a recently obtained bound, 23, due to Cranston, Lafferty and Song.

Keywords

proper coloringodd coloring1-planar graph
CLC number: O157.5 Document code: A Article ID: 2096-7675(2023)03-0267-07

References

【1】
【1】
 
 
Crossref Google Scholar
Journal of Xinjiang University(Natural Science Edition in Chinese and English)
Volume 40 Issue 3,
May 2023
Pages 267-273
DOI: 10.13568/j.cnki.651094.651316.2022.07.01.0001

{{item.num}}

Comments on this article

Go to comment

< Back to all reports

Review Status: {{reviewData.commendedNum}} Commended , {{reviewData.revisionRequiredNum}} Revision Required , {{reviewData.notCommendedNum}} Not Commended Under Peer Review

Review Comment

Cite this Report
Close
Close
Cite this article:
GUO C, WU B. Odd Chromatic Number of a 1-Planar Graph is at Most 21. Journal of Xinjiang University(Natural Science Edition in Chinese and English), 2023, 40(3): 267-273. https://doi.org/10.13568/j.cnki.651094.651316.2022.07.01.0001

493

Views

25

Downloads

0

Crossref
Received: 01 July 2022
Published: 01 May 2023
© 2023 Journal of Xinjiang University (Natural Science Edition in Chinese and English)