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arXiv · 1605.08905

A Study of $k$-dipath Colourings of Oriented Graphs

Christopher Duffy·Gary MacGillivray·Éric Sopena
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Abstract

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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Christopher Duffy, Gary MacGillivray, Éric Sopena. 2016-05-28. A Study of $k$-dipath Colourings of Oriented Graphs. https://doi.org/10.23638/dmtcs-20-1-6

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