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- W4285484079 abstract "We study the minimum size $f$ of a feedback vertex set in directed and undirected $n$-vertex graphs of given degeneracy or treewidth. In the undirected setting the bound $frac{k-1}{k+1}n$ is known to be tight for graphs with bounded treewidth $k$ or bounded odd degeneracy $k$. We show that neither of the easy upper and lower bounds $frac{k-1}{k+1}n$ and $frac{k}{k+2}n$ can be exact for the case of even degeneracy. More precisely, for even degeneracy $k$ we prove that $f < frac{k}{k+2}n$ and for every $epsilon>0$, there exists a $k$-degenerate graph for which $fgeq frac{3k-2}{3k+4}n -epsilon$.
 For directed graphs of bounded degeneracy $k$, we prove that $fleqfrac{k-1}{k+1}n$ and that this inequality is strict when $k$ is odd. For directed graphs of bounded treewidth $kgeq 2$, we show that $f leq frac{k}{k+3}n$ and for every $epsilon>0$, there exists a $k$-degenerate graph for which $fgeq frac{k-2lfloorlog_2(k)rfloor}{k+1}n -epsilon$. Further, we provide several constructions of low degeneracy or treewidth and large $f$." @default.
- W4285484079 created "2022-07-15" @default.
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- W4285484079 date "2022-10-21" @default.
- W4285484079 modified "2023-10-13" @default.
- W4285484079 title "Feedback Vertex Sets in (Directed) Graphs of Bounded Degeneracy or Treewidth" @default.
- W4285484079 doi "https://doi.org/10.37236/10914" @default.
- W4285484079 hasPublicationYear "2022" @default.
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