The Odd Chromatic Number of a Planar Graph is at Most 8

Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex x ∈ V ( G ) there exists a colour c appearing an odd number of times in its neighbourhood N ( x ). Petruševski and Škreko...

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Bibliographic Details
Published in:Graphs and combinatorics Vol. 39; no. 2; p. 28
Main Authors: Petr, Jan, Portier, Julien
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.04.2023
Springer Nature B.V
Subjects:
Combinatorics
Engineering Design
Forests
Graph coloring
Graphs
Mathematics
Mathematics and Statistics
Original Paper
colouring
Planar graph
discharging method
odd colouring
ISSN:0911-0119, 1435-5914
Online Access:Get full text
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Summary:Petruševski and Škrekovski recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph G is said to be odd if for each non-isolated vertex x ∈ V ( G ) there exists a colour c appearing an odd number of times in its neighbourhood N ( x ). Petruševski and Škrekovski proved that for any planar graph G there is an odd colouring using at most 9 colours and, together with Caro, showed that 8 colours are enough for a significant family of planar graphs. We show that 8 colours suffice for all planar graphs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-023-02617-z