Abstract
The Feedback Vertex Set problem asks whether a graph contains q vertices meeting all its cycles. This is not a local property, in the sense that we cannot check if q vertices meet all cycles by looking only at their neighbors. Dynamic programming algorithms for problems based on non-local properties are usually more complicated. In this paper, given a graph G of cliquewidth cw and a cw-expression of G, we solve the Minimum Feedback Vertex Set problem in time \(O(n^22^{2cw^2 \log cw})\). Our algorithm applies a non-standard dynamic programming on a so-called k-module decomposition of a graph, as defined by Rao [26], which is easily derivable from a k-expression of the graph. The related notion of module-width of a graph is tightly linked to both cliquewidth and nlc-width, and in this paper we give an alternative equivalent characterization of module-width.
Supported by the Norwegian Research Council, project PARALGO.
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Bui-Xuan, BM., Telle, J.A., Vatshelle, M. (2009). Feedback Vertex Set on Graphs of Low Cliquewidth. In: Fiala, J., Kratochvíl, J., Miller, M. (eds) Combinatorial Algorithms. IWOCA 2009. Lecture Notes in Computer Science, vol 5874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10217-2_14
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