Abstract
In this paper we study a generalization of classic Feedback Vertex Set problem in the realm of multivariate complexity analysis. We say that a graph F is an l-forest if we can delete at most l edges from F to get a forest. That is, F is at most l edges away from being a forest. In this paper we introduce the Almost Forest Deletion problem, where given a graph G and integers k and l, the question is whether there exists a subset of at most k vertices such that its deletion leaves us an l-forest. We show that this problem admits an algorithm with running time \(2^{{\mathcal {O}}(l+k)}n^{{\mathcal {O}}(1)}\) and a kernel of size \({\mathcal {O}}(kl(k+l))\). We also show that the problem admits a \(c^{\mathbf {tw}}n^{{\mathcal {O}}(1)}\) algorithm on bounded treewidth graphs, using which we design a subexponential algorithm for the problem on planar graphs.
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Rai, A., Saurabh, S. (2015). Bivariate Complexity Analysis of Almost Forest Deletion . In: Xu, D., Du, D., Du, D. (eds) Computing and Combinatorics. COCOON 2015. Lecture Notes in Computer Science(), vol 9198. Springer, Cham. https://doi.org/10.1007/978-3-319-21398-9_11
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