Odd Colourings of Graph Products
Vida Dujmovi\'c, Pat Morin, and Saeed Odak

TL;DR
This paper introduces bounds on the odd colouring number for graphs with product structure, including $k$-planar graphs, thereby answering a previously open question in graph theory.
Contribution
It establishes that graphs with certain product structures have bounded odd-colouring numbers, notably applying this to $k$-planar graphs.
Findings
Graphs with product structure have bounded odd-colouring number.
$k$-planar graphs have bounded odd-colouring number.
Answers an open question by Cranston, Lafferty, and Song.
Abstract
The odd colouring number is a new graph parameter introduced by Petru\v{s}evski and \v{S}krekovski. In this note, we show that graphs with so called product structure have bounded odd-colouring number. By known results on the product structure of -planar graphs, this implies that -planar graphs have bounded odd-colouring number, which answers a question of Cranston, Lafferty, and Song.
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Limits and Structures in Graph Theory
