DROPS.MEMICS.2009.2350.pdf
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The Parameterized Complexity of Oriented Colouring
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Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09) (MEMICS 2009)
Series: Open Access Series in Informatics (OASIcs) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2009-12-15
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Robert Ganian. The Parameterized Complexity of Oriented Colouring. In Annual Doctoral Workshop on Mathematical and Engineering Methods in Computer Science (MEMICS'09). Open Access Series in Informatics (OASIcs), Volume 13, pp. 88-95, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DROPS.MEMICS.2009.2350
https://doi.org/10.4230/DROPS.MEMICS.2009.2350
Abstract
The oriented colouring problem is intuitive and related to
undirected colouring, yet remains NP-hard even on digraph classes
with bounded traditional directed width measures.
Recently we have also proved that it remains NP-hard
in otherwise severely restricted digraph classes.
However, unlike most other problems on directed graphs, the oriented colouring
problem is not directly transferable to undirected graphs.
In the article we look at the parameterized complexity of computing the oriented colouring
of digraphs with bounded undirected width parameters, whereas the parameters
``forget'' about the orientations of arcs and treat them as edges.
Specifically, we provide new complexity results for computing oriented colouring
on digraphs of bounded undirected rank-width and a new algorithm for this problem
on digraphs of bounded undirected tree-width.
Keywords
- Oriented colouring
- tree-width
- rank-width
- parameterized algorithms
- graphs
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