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.

Source : oai:arXiv.org:1605.08905

Volume: Vol. 20 no. 1

Section: Graph Theory

Published on: February 1, 2018

Submitted on: August 3, 2017

Keywords: Computer Science - Discrete Mathematics,Mathematics - Combinatorics,05C15, 05C20, 05C60,F.2.2,G.2.2

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