Geodesic
A Study of $k$-dipath Colourings of Oriented Graphs
Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1.

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We examine $t$-colourings of oriented graphs in which, for a fixed integer $k \geq 1$, vertices joined by a directed path of length at most $k$ must be assigned different colours. A homomorphism model that extends the ideas of Sherk for the case $k=2$ is described. Dichotomy theorems for the complexity of the problem of deciding, for fixed $k$ and $t$, whether there exists such a $t$-colouring are proved. 
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     author = {Duffy, Christopher and MacGillivray, Gary and Sopena, \'Eric},
     title = {A {Study} of $k$-dipath {Colourings} of {Oriented} {Graphs}},
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Duffy, Christopher; MacGillivray, Gary; Sopena, Éric. A Study of $k$-dipath Colourings of Oriented Graphs. Discrete mathematics & theoretical computer science, Tome 20 (2018) no. 1. doi : 10.23638/DMTCS-20-1-6. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-20-1-6/

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