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arXiv · 2201.12381

The odd chromatic number of a planar graph is at most 8

Jan Petr·Julien Portier
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Abstract

Petru\v{s}evski and \v{S}krekovski \cite{odd9} recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph $G$ is said to be \emph{odd} if for each non-isolated vertex $x \in V(G)$ there exists a colour $c$ appearing an odd number of times in $N(x)$. Petru\v{s}evski and \v{S}krekovski proved that for any planar graph $G$ there is an odd colouring using at most $9$ colours and, together with Caro \cite{oddremarks}, showed that $8$ colours are enough for a significant family of planar graphs. We show that $8$ colours suffice for all planar graphs.

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Jan Petr, Julien Portier. 2022-01-28. The odd chromatic number of a planar graph is at most 8. https://doi.org/10.1007/s00373-023-02617-z

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