# Article

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Keywords:
graph colourings; paths; Hasse-Gallai-Roy Theorem
Summary:
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.
References:
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