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Colorings with neighborhood parity condition
ID
Petruševski, Mirko
(
Author
),
ID
Škrekovski, Riste
(
Author
)
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MD5: 1A931325A3495F66918020D76A1C082F
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https://www.sciencedirect.com/science/article/pii/S0166218X22002803
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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
UDC:
519.17
ISSN on article:
0166-218X
DOI:
10.1016/j.dam.2022.07.018
COBISS.SI-ID:
139308803
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
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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