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Colorings with neighborhood parity condition
ID Petruševski, Mirko (Author), ID Škrekovski, Riste (Author)

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Abstract
In this short paper, we introduce a new vertex coloring whose motivation comes from our series on odd edge-colorings of graphs. A proper vertex coloring $\varphi$ of a graph $G$ is said to be odd if for each non-isolated vertex $x \in V(G)$ there exists a color $c$ such that $\varphi^{-1}(c) \cap N(x)$ is odd-sized. We prove that every simple planar graph admits an odd 9-coloring, and conjecture that 5 colors always suffice.

Language:English
Keywords:planar graphs, neighborhood, proper coloring, odd coloring
Work type:Article
Typology:1.01 - Original Scientific Article
Organization:FMF - Faculty of Mathematics and Physics
Publication status:Published
Publication version:Version of Record
Year:2022
Number of pages:Str. 385-391
Numbering:Vol. 321
PID:20.500.12556/RUL-144060 This link opens in a new window
UDC:519.17
ISSN on article:0166-218X
DOI:10.1016/j.dam.2022.07.018 This link opens in a new window
COBISS.SI-ID:139308803 This link opens in a new window
Publication date in RUL:30.01.2023
Views:545
Downloads:81
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Record is a part of a journal

Title:Discrete applied mathematics
Shortened title:Discrete appl. math.
Publisher:Elsevier
ISSN:0166-218X
COBISS.SI-ID:25342464 This link opens in a new window

Licences

License:CC BY 4.0, Creative Commons Attribution 4.0 International
Link:http://creativecommons.org/licenses/by/4.0/
Description:This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

Language:Slovenian
Keywords:ravninski grafi, soseščina, dobro barvanje, liho barvanje

Projects

Funder:ARRS - Slovenian Research Agency
Project number:P1-0383
Name:Kompleksna omrežja

Funder:ARRS - Slovenian Research Agency
Project number:J1-3002
Name:Prirejanja in barvanja povezav v kubičnih grafih

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