Abstract
The Restricted Subset Feedback Vertex Set problem (R-SFVS) takes a graph $$G = (V, E)$$ , a terminal set $$T \subseteq V$$ , and an integer k as the input. The task is to determine whether there exists a subset $$S \subseteq V \setminus T$$ of at most k vertices, after deleting which no terminal in T is contained in a cycle in the remaining graph. R-SFVS is $$\textsf {NP}$$ -complete even when the input graph is restricted to chordal graphs. In this paper, we show that R-SFVS in chordal graphs can be solved in time $$\mathcal {O}(1.1550^{|V|})$$ , significantly improving all the previous results. As a by-product, we prove that the Maximum Independent Set problem parameterized by the edge clique cover number is fixed-parameter tractable. Furthermore, by using a simple reduction from R-SFVS to Vertex Cover, we obtain a $$1.2738^{k}|V|^{\mathcal {O}(1)}$$ -time parameterized algorithm and an $$\mathcal {O}(k^{2})$$ -kernel for R-SFVS in chordal graphs.
Published Version
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