Odd colouring on the torus

Harry Metrebian

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arXiv · 2205.04398

Odd colouring on the torus

Harry Metrebian

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Abstract

A proper vertex-colouring of a simple graph $G$ is said to be odd if, for every non-isolated vertex $v$ of $G$, some colour appears an odd number of times in the neighbourhood of $v$. We show that if $G$ embeds in the torus, then it admits a proper odd vertex-colouring with at most $9$ colours.

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Harry Metrebian. 2022-05-09. Odd colouring on the torus. https://arxiv.org/abs/2205.04398

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