Abstract
In this survey, a number of results on the fixed-parameter tractability of treewidth and pathwidth are discussed. Some emphasis is placed on older results, and proofs that show that treewidth and pathwidth are fixed-parameter tractable. Also, a linear-time algorithm for testing if a graph has pathwidth at most some given constant is discussed in more detail.
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Bodlaender, H.L. (2012). Fixed-Parameter Tractability of Treewidth and Pathwidth. In: Bodlaender, H.L., Downey, R., Fomin, F.V., Marx, D. (eds) The Multivariate Algorithmic Revolution and Beyond. Lecture Notes in Computer Science, vol 7370. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30891-8_12
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