Abstract
The treewidth and cliquewidth of a graph are central notions in graph theory and graph algorithms. Many NP-hard problems become tractable when the treewidth or cliquewidth of the input graph is bounded by a constant. In this talk I will briefly survey the known algorithmic results for graphs of bounded treewidth and cliquewidth, and give an overview of a line of work that explores the limits of tractability of problems on graphs of bounded treewidth or cliquewidth. Specifically, we will consider the following questions:
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Which problems are solvable in polynomial time on graphs of bounded treewidth, but require that the degree of the polynomial grows with the treewidth?
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Which problems are harder on bounded cliquewidth graphs than on bounded treewidth graphs?
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Can the known algorithms for problems on graphs of bounded treewidth and cliquewidth be improved?
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Lokshtanov, D. (2010). Algorithmic Lower Bounds for Problems on Decomposable Graphs. In: Hliněný, P., Kučera, A. (eds) Mathematical Foundations of Computer Science 2010. MFCS 2010. Lecture Notes in Computer Science, vol 6281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15155-2_4
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DOI: https://doi.org/10.1007/978-3-642-15155-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15154-5
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