A Study of k-dipath Colourings of Oriented Graphs
Résumé
We examine t-colourings of oriented graphs in which, for a fixed integer k ≥ 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.