New Results on the Complexity of Oriented Colouring on Restricted Digraph Classes

Authors:
Robert Ganian;Petr Hliněný
Affiliations:
Faculty of Informatics, Masaryk University, Brno, Czech Republic;Faculty of Informatics, Masaryk University, Brno, Czech Republic
Venue:
SOFSEM '10 Proceedings of the 36th Conference on Current Trends in Theory and Practice of Computer Science
Year:
2009

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Abstract

Oriented colouring is a quite intuitive generalization of undirected colouring, yet the problem remains NP-hard even on digraph classes with bounded usual directed width measures. In light of this fact, one might ask whether new width measures are required for efficient dealing with this problem or whether further restriction of traditional directed width measures such as DAG-width would suffice. The K-width and DAG-depth measures (introduced by [Ganian et al, IWPEC'09]) are ideal candidates for tackling this question: They are both closely tied to the cops-and-robber games which inspire and characterize the most renowned directed width measures, while at the same time being much more restrictive.In this paper, we look at the oriented colouring problem on digraphs of bounded K-width and of bounded DAG-depth. We provide new polynomial algorithms for solving the problem on "small" instances as well as new strong hardness results showing that the input restrictions required by our algorithms are in fact "tight".