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- W4300303019 abstract "For a finite collection of graphs ${cal F}$, the ${cal F}$-M-DELETION problem consists in, given a graph $G$ and an integer $k$, deciding 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. We are interested in the parameterized complexity of ${cal F}$-M-DELETION when the parameter is the treewidth of $G$, denoted by $tw$. Our objective is to determine, for a fixed ${cal F}$, the smallest function $f_{{cal F}}$ such that {${cal F}$-M-DELETION can be solved in time $f_{{cal F}}(tw) cdot n^{O(1)}$ on $n$-vertex graphs. We prove that $f_{{cal F}}(tw) = 2^{2^{O(tw cdotlog tw)}}$ for every collection ${cal F}$, that $f_{{cal F}}(tw) = 2^{O(tw cdotlog tw)}$ if ${cal F}$ contains a planar graph, and that $f_{{cal F}}(tw) = 2^{O(tw)}$ if in addition the input graph $G$ is planar or embedded in a surface. We also consider the version of the problem where the graphs in ${cal F}$ are forbidden as topological minors, called ${cal F}$-TM-DELETION. We prove similar results for this problem, except that in the last two algorithms, instead of requiring ${cal F}$ to contain a planar graph, we need it to contain a subcubic planar graph. This is the first of a series of articles on this topic." @default.
- W4300303019 created "2022-10-03" @default.
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- W4300303019 date "2017-04-24" @default.
- W4300303019 modified "2023-09-26" @default.
- W4300303019 title "Hitting minors on bounded treewidth graphs. I. General upper bounds" @default.
- W4300303019 doi "https://doi.org/10.48550/arxiv.1704.07284" @default.
- W4300303019 hasPublicationYear "2017" @default.
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