# Feedback vertex set on graphs of low cliquewidth

2 APR - Algorithmes, Programmes et Résolution
LIP6 - Laboratoire d'Informatique de Paris 6
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 clique-width $cw$ and a $cw$-expression of $G$, we solve the Minimum Feedback Vertex Set problem in time $O(n^22^{O(cw \log cw)})$. Our algorithm applies dynamic programming on a so-called $k$-module decomposition of a graph, as defined by Rao \cite{R08}, 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 clique-width and NLC-width, and in this paper we give an alternative equivalent characterization of module-width.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-00640643
Contributor : Binh-Minh Bui-Xuan <>
Submitted on : Monday, November 14, 2011 - 8:14:35 AM
Last modification on : Tuesday, June 30, 2020 - 3:34:02 PM

### Identifiers

• HAL Id : hal-00640643, version 1

### Citation

Binh-Minh Bui-Xuan, Ondra Suchy, Jan Arne Telle, Martin Vatshelle. Feedback vertex set on graphs of low cliquewidth. European Journal of Combinatorics, Elsevier, 2013, 34 (3), pp.666-679. ⟨hal-00640643⟩

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