An FPT algorithm for Tree Deletion Set

We give a 5n time fixed-parameter algorithm for determining whether a given undirected graph on n vertices has a subset of at most k vertices whose deletion results in a tree. Such a subset is a restricted form of a feedback vertex set. While parameterized complexity of feedback vertex set problem and several of its variations have been well studied, to the best of our knowledge, this is the first fixed-parameter algorithm for this version of feedback vertex set. Submitted: May 2013 Reviewed: September 2013 Revised: October 2013 Accepted: October 2013 Final: October 2013 Published: November 2013 Article type: Regular paper Communicated by: S. K. Ghosh A preliminary version of this work appeared in the proceedings of WALCOM 2013 [21]. Part of the work of the third author was done while with the Universität des Saarlandes, Saarbrücken, supported by the DFG Cluster of Excellence on Multimodal Computing and Interaction (MMCI) and DFG project DARE (GU 1023/1-2), and while visiting IMSc Chennai, supported by the Indo-German Max Planck Center for Computer Science (IMPECS). E-mail addresses: vraman@imsc.res.in (Venkatesh Raman) saket@imsc.res.in (Saket Saurabh) ondrej.suchy@fit.cvut.cz (Ondřej Suchý) 616 Raman, Saurabh, Suchý An FPT algorithm for Tree Deletion Set

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