The Parameterised Complexity of List Problems on Graphs of Bounded Treewidth

Abstract

We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable, parameterised by treewidth, whereas List Hamilton Path is W[1]-hard, even parameterised by pathwidth. These results resolve two open questions of Fellows, Fomin, Lokshtanov, Rosamond, Saurabh, Szeider and Thomassen (2011).

arXiv commentAuthor final version, to appear in Information and Computation. Changes from previous version include improved literature references and restructured proof in Section 3