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Orientations and $3$ -colourings of graphs

Vincent Chouinard-Prévost; Alexandre Côté; Claude Tardif — 2004

Commentationes Mathematicae Universitatis Carolinae

We provide the list of all paths with at most $16$ arcs with the property that if a graph $G$ admits an orientation $\vec{G}$ such that one of the paths in our list admits no homomorphism to $\vec{G}$ , then $G$ is $3$ -colourable.

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