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- W3135652805 abstract "For a finite collection of graphs ${cal F}$, the ${cal F}$-M-DELETION (resp. ${cal F}$-TM-DELETION) problem consists in, given a graph $G$ and an integer $k$, decide whether there exists $S subseteq V(G)$ with $|S| leq k$ such that $G setminus S$ does not contain any of the graphs in ${cal F}$ as a minor (resp. topological minor). We are interested in the parameterized complexity of both problems when the parameter is the treewidth of $G$, denoted by $tw$, and specifically in the cases where ${cal F}$ contains a single connected planar graph $H$. We present algorithms running in time $2^{O(tw)} cdot n^{O(1)}$, called single-exponential, when $H$ is either $P_3$, $P_4$, $C_4$, the paw, the chair, and the banner for both ${H}$-M-DELETION and ${H}$-TM-DELETION, and when $H=K_{1,i}$, with $i geq 1$, for ${H}$-TM-DELETION. Some of these algorithms use the rank-based approach introduced by Bodlaender et al. [Inform Comput, 2015]. This is the second of a series of articles on this topic, and the results given here together with other ones allow us, in particular, to provide a tight dichotomy on the complexity of ${H}$-M-DELETION in terms of $H$." @default.
- W3135652805 created "2021-03-15" @default.
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- W3135652805 date "2021-03-11" @default.
- W3135652805 modified "2023-09-25" @default.
- W3135652805 title "Hitting minors on bounded treewidth graphs. II. Single-exponential algorithms" @default.
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